Abstract

We compare volume-consumption characteristics of free-space and guided-wave optical interconnections. System volume consumption is used as a fundamental measure of various point-to-point space-invariant and space-variant interconnections of two-dimensional arrays of N 1/2 × N 1/2 points. We show that, in free-space and space-invariant situations, although volume consumption for macroaperture optics is O 1(N 3/2), where O denotes the order, it is only O 2(N) for microaperture optics. For free-space and space-variant operations only microaperture optics is possible without fundamental power losses. The corresponding minimum volume consumption is O 3(N 3). We show that single microaperture-per-channel implementations of either space-invariant or space-variant operations are, in general, more volume efficient than are their two-cascade microaperture-per-channel counterparts. We also show that, for minimizing volume consumption, the optimum relative apertures F#opt for space-variant optical elements are, respectively, (5N)1/2/4 for a single microaperture-per-channel geometry and (5N)1/2/2 for a two-cascade microaperture-per-channel geometry. In guided-wave or fiber interconnect cases our study shows that the volume consumption for space-invariant and space-variant operations is O 4(N), with O 4 < O 2, and O 5(N 3/2), respectively. Thus an important conclusion of the study is that free-space optics is less volume efficient than is guided-wave optics in both space-invariant and space-variant interconnect applications.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. Athale, “Optical interconnections for vlsi systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  2. F. E. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
    [CrossRef]
  3. D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett. 14, 146–148 (1989).
    [CrossRef] [PubMed]
  4. R. K. Kostuk, J. W. Goodman, L. Hesselink, “Optical imaging applied to microelectronic chip-to-chip interconnections,” Appl. Opt. 24, 2851–2858 (1985).
    [CrossRef] [PubMed]
  5. H. M. Ozaktas, J. W. Goodman, “Lower bound for the communication volume required for an optically interconnected array of points,” J. Opt. Soc. Am. A 7, 2100–2106 (1990).
    [CrossRef]
  6. K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Diffractive optics applied to free-space optical interconnects,” Appl. Opt. 33, 3670–3682 (1994).
    [CrossRef] [PubMed]
  7. H. M. Ozaktas, H. Urey, A. W. Lohmann, “Scaling of diffractive and refractive lenses for optical computing and interconnections,” Appl. Opt. 33, 3782–3789 (1994).
    [CrossRef] [PubMed]
  8. N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
    [CrossRef] [PubMed]
  9. A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28, 4996–4998 (1989).
    [CrossRef] [PubMed]
  10. 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]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2, pp. 4–29.
  12. F. C. Allard, Fiber Optics Handbook (McGraw-Hill, New York, 1989), Chap. 1, pp. 1–50.
  13. M. A. Paesler, P. J. Moyer, Near-Field Optics (Wiley, New York, 1996), Chap. 3, pp. 33–66.
  14. H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
    [CrossRef]
  15. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
    [CrossRef]
  16. W. V. Schempp, “Fiber optic imaging: an introduction,” in SPIE Short Course Notes-SC33 (SPIE, Bellingham, Wash., 1995).
  17. Y. Li, T. Wang, H. Kosaka, S. Kawai, K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt. 35, 6920–6933 (1996).
    [CrossRef] [PubMed]
  18. H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
    [CrossRef]
  19. K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
    [CrossRef]
  20. J. Ai, Y. Li, “Polymer fiber-image-guide–based embedded optical circuit board,” Appl. Opt. 38, 325–332 (1999).
    [CrossRef]
  21. C.-L. Wu, T. Y. Feng, Tutorial: Interconnection Networks for Parallel and Distributed Processing (IEEE Computer Society Press, Piscataway, N.J., 1984), Chap. 3.
  22. F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt. 33, 1601–1618 (1994).
    [CrossRef] [PubMed]
  23. H. M. Ozaktas, D. Mendlovic, “Multistage optical interconnection architectures with the least possible growth of system size,” Opt. Lett. 18, 296–298 (1993).
    [CrossRef] [PubMed]
  24. G. Onal, A. Altintas, H. M. Ozaktas, “Computer-aided analysis and simulation of complex passive integrated optical circuits of arbitrary rectilinear topology,” Opt. Eng. 33, 1696–1603 (1994).
    [CrossRef]
  25. M. W. Haney, M. Christensen, “Sliding banyan network,” J. Lightwave Technol. 14, 765–774 (1996).
    [CrossRef]
  26. J. Popelek, Y. Li, “Free-space-fiber hybrid distributed optical cross-connect interconnect module,” Opt. Lett. 24, 142–144 (1999).
    [CrossRef]
  27. J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
    [CrossRef] [PubMed]
  28. Y. Li, “Some fundamental issues of optical interconnects,” in Advances in Electronic Packaging 1997, E. Suhir, Y. C. Lee, eds. (AMSE Publishing, New York, 1997), pp. 793–802.
  29. D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, The Netherlands, 1961), Vol. 1, pp. 109–153.
    [CrossRef]

1999 (2)

1998 (1)

H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
[CrossRef]

1997 (2)

H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
[CrossRef]

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

1996 (3)

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
[CrossRef]

M. W. Haney, M. Christensen, “Sliding banyan network,” J. Lightwave Technol. 14, 765–774 (1996).
[CrossRef]

Y. Li, T. Wang, H. Kosaka, S. Kawai, K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt. 35, 6920–6933 (1996).
[CrossRef] [PubMed]

1994 (4)

1993 (1)

1992 (1)

1991 (1)

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

1990 (1)

1989 (4)

1985 (1)

1984 (1)

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

Ai, J.

Allard, F. C.

F. C. Allard, Fiber Optics Handbook (McGraw-Hill, New York, 1989), Chap. 1, pp. 1–50.

Altintas, A.

G. Onal, A. Altintas, H. M. Ozaktas, “Computer-aided analysis and simulation of complex passive integrated optical circuits of arbitrary rectilinear topology,” Opt. Eng. 33, 1696–1603 (1994).
[CrossRef]

Athale, R.

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

Christensen, M.

M. W. Haney, M. Christensen, “Sliding banyan network,” J. Lightwave Technol. 14, 765–774 (1996).
[CrossRef]

Cloonan, T. J.

Davidson, N.

Dorsch, R. G.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
[CrossRef]

Esener, S. C.

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

Fainman, Y.

Feldman, M. R.

Feng, T. Y.

C.-L. Wu, T. Y. Feng, Tutorial: Interconnection Networks for Parallel and Distributed Processing (IEEE Computer Society Press, Piscataway, N.J., 1984), Chap. 3.

Ferreira, C.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
[CrossRef]

Friesem, A. A.

Gabor, D.

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, The Netherlands, 1961), Vol. 1, pp. 109–153.
[CrossRef]

Ghaemi, H. F.

H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
[CrossRef]

Goodman, J. W.

Guest, C. C.

Haney, M. W.

M. W. Haney, M. Christensen, “Sliding banyan network,” J. Lightwave Technol. 14, 765–774 (1996).
[CrossRef]

Hasman, E.

Hesselink, L.

Hinton, H. S.

Huang, A.

Igasaki, Y.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

Jahns, J.

Kajita, M.

H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
[CrossRef]

Kaneda, K.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

Kasahara, K.

Kawai, S.

Kiamilev, F. E.

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

Kitayama, K.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

Kosaka, H.

H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
[CrossRef]

Y. Li, T. Wang, H. Kosaka, S. Kawai, K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt. 35, 6920–6933 (1996).
[CrossRef] [PubMed]

Kostuk, R. K.

Krishnamoorthy, A. V.

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

Kung, S.-Y.

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

Lee, S. H.

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Diffractive optics applied to free-space optical interconnects,” Appl. Opt. 33, 3670–3682 (1994).
[CrossRef] [PubMed]

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

Lentine, A. L.

Leonberger, F. J.

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

Li, Y.

J. Ai, Y. Li, “Polymer fiber-image-guide–based embedded optical circuit board,” Appl. Opt. 38, 325–332 (1999).
[CrossRef]

J. Popelek, Y. Li, “Free-space-fiber hybrid distributed optical cross-connect interconnect module,” Opt. Lett. 24, 142–144 (1999).
[CrossRef]

H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
[CrossRef]

H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
[CrossRef]

Y. Li, T. Wang, H. Kosaka, S. Kawai, K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt. 35, 6920–6933 (1996).
[CrossRef] [PubMed]

Y. Li, “Some fundamental issues of optical interconnects,” in Advances in Electronic Packaging 1997, E. Suhir, Y. C. Lee, eds. (AMSE Publishing, New York, 1997), pp. 793–802.

Lohmann, A. W.

Marchand, P.

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Diffractive optics applied to free-space optical interconnects,” Appl. Opt. 33, 3670–3682 (1994).
[CrossRef] [PubMed]

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

McCormick, F. B.

Mendlovic, D.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Multistage optical interconnection architectures with the least possible growth of system size,” Opt. Lett. 18, 296–298 (1993).
[CrossRef] [PubMed]

Miller, D. A. B.

Morrison, R. L.

Moyer, P. J.

M. A. Paesler, P. J. Moyer, Near-Field Optics (Wiley, New York, 1996), Chap. 3, pp. 33–66.

Nakamura, M.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

Novotny, R. A.

Onal, G.

G. Onal, A. Altintas, H. M. Ozaktas, “Computer-aided analysis and simulation of complex passive integrated optical circuits of arbitrary rectilinear topology,” Opt. Eng. 33, 1696–1603 (1994).
[CrossRef]

Ozaktas, H. M.

Paesler, M. A.

M. A. Paesler, P. J. Moyer, Near-Field Optics (Wiley, New York, 1996), Chap. 3, pp. 33–66.

Popelek, J.

Sasian, J. M.

Schempp, W. V.

W. V. Schempp, “Fiber optic imaging: an introduction,” in SPIE Short Course Notes-SC33 (SPIE, Bellingham, Wash., 1995).

Sugimoto, Y.

H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
[CrossRef]

Thio, T.

H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
[CrossRef]

Urey, H.

Urquhart, K. S.

Wang, T.

H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
[CrossRef]

Y. Li, T. Wang, H. Kosaka, S. Kawai, K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt. 35, 6920–6933 (1996).
[CrossRef] [PubMed]

Wu, C.-L.

C.-L. Wu, T. Y. Feng, Tutorial: Interconnection Networks for Parallel and Distributed Processing (IEEE Computer Society Press, Piscataway, N.J., 1984), Chap. 3.

Zalevsky, Z.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
[CrossRef]

Appl. Opt. (10)

R. K. Kostuk, J. W. Goodman, L. Hesselink, “Optical imaging applied to microelectronic chip-to-chip interconnections,” Appl. Opt. 24, 2851–2858 (1985).
[CrossRef] [PubMed]

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]

A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28, 4996–4998 (1989).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
[CrossRef] [PubMed]

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Diffractive optics applied to free-space optical interconnects,” Appl. Opt. 33, 3670–3682 (1994).
[CrossRef] [PubMed]

H. M. Ozaktas, H. Urey, A. W. Lohmann, “Scaling of diffractive and refractive lenses for optical computing and interconnections,” Appl. Opt. 33, 3782–3789 (1994).
[CrossRef] [PubMed]

J. Ai, Y. Li, “Polymer fiber-image-guide–based embedded optical circuit board,” Appl. Opt. 38, 325–332 (1999).
[CrossRef]

Y. Li, T. Wang, H. Kosaka, S. Kawai, K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt. 35, 6920–6933 (1996).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt. 33, 1601–1618 (1994).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

H. F. Ghaemi, Y. Li, T. Thio, T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72, 1137–1139 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Kosaka, M. Kajita, Y. Li, Y. Sugimoto, “A two-dimensional optical parallel transmission using a vertical-cavity surface-emitting laser array module and an image fiber,” IEEE Photon. Technol. Lett. 9, 253–255 (1997).
[CrossRef]

J. Lightwave Technol. (3)

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

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

M. W. Haney, M. Christensen, “Sliding banyan network,” J. Lightwave Technol. 14, 765–774 (1996).
[CrossRef]

J. Opt. Am. Soc. A (1)

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “About the space–bandwidth product of optical signals and systems,” J. Opt. Am. Soc. A 13, 470–473 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

G. Onal, A. Altintas, H. M. Ozaktas, “Computer-aided analysis and simulation of complex passive integrated optical circuits of arbitrary rectilinear topology,” Opt. Eng. 33, 1696–1603 (1994).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

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

Other (7)

Y. Li, “Some fundamental issues of optical interconnects,” in Advances in Electronic Packaging 1997, E. Suhir, Y. C. Lee, eds. (AMSE Publishing, New York, 1997), pp. 793–802.

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, The Netherlands, 1961), Vol. 1, pp. 109–153.
[CrossRef]

W. V. Schempp, “Fiber optic imaging: an introduction,” in SPIE Short Course Notes-SC33 (SPIE, Bellingham, Wash., 1995).

C.-L. Wu, T. Y. Feng, Tutorial: Interconnection Networks for Parallel and Distributed Processing (IEEE Computer Society Press, Piscataway, N.J., 1984), Chap. 3.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2, pp. 4–29.

F. C. Allard, Fiber Optics Handbook (McGraw-Hill, New York, 1989), Chap. 1, pp. 1–50.

M. A. Paesler, P. J. Moyer, Near-Field Optics (Wiley, New York, 1996), Chap. 3, pp. 33–66.

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 (12)

Fig. 1
Fig. 1

Schematics of the cases studied: (a) space-invariant cases, (b) FV case, (c) GV case. L, system length; V, system volume; N, number of channels. Subscripts: FI, free space and space invariant; FV, free space and space variant; GI, guided wave and space invariant; and GV, guided wave and space variant.

Fig. 2
Fig. 2

Two space-invariant imaging systems that use macro-optics: (a) a two lens per channel system, (b) a single lens per channel system.

Fig. 3
Fig. 3

Drawings equivalent to those of Fig. 2. The imaging operation is decomposed into a sequence of (a) beam-collimation, deflection, opposite deflection, and focusing operations and (b) beam-collimation and focusing operations.

Fig. 4
Fig. 4

Two micro-optics interconnect systems that use multifaceted optical components: (a) two lenses–holograms per channel, (b) a single lens–hologram per channel.

Fig. 5
Fig. 5

Drawings equivalent to those of Fig. 4: (a) two lenses–holograms per channel, (b) a single lens–hologram per channel. In (a) diffracted beams at the first lens–hologram pair could spill over to neighboring facets.

Fig. 6
Fig. 6

(a) N = 16 banyan interconnect topology for a 1-D array. (b) The same topology for a 2-D array.

Fig. 7
Fig. 7

(a) N = 16 back-to-back (except for the final stage) banyan-based reconfigurable nonblocking interconnect for a 1-D array. (b) The same interconnect for a 2-D array.

Fig. 8
Fig. 8

Geometry and parameters for a bent waveguide. R, average bending radius; α, half-bending angle; Δl′, bending-induced length penalty.

Fig. 9
Fig. 9

(a) Transmissive 4f optical system. (b) A folded 4f system with one reflection. (c) A folded (planar) 4f system with five reflections. As the number of reflections increases, both the volume and the number of channels decrease.

Fig. 10
Fig. 10

Plots of the volume consumption for various FI and FV cases. A value of F# = 1 is used for four FI cases: MFI(a), MFI(b), μFI(a), and μFI(b). An optimized F# is used for μFV(a), μFV(b), Eq. (42), and Eq. (43).

Fig. 11
Fig. 11

Plots of the volume consumption for GI and FI cases. A value of F# = 1 is used for the cases of μFI(a) and μFI(b). Values of l = λ and γ = 4 are used for the GI case.

Fig. 12
Fig. 12

Plots of the volume consumption for GV and FV cases. The two GV curves are plots of the lower-bound (one without considering the bending penalty) case and the case of k = 104 and γ = 4. The two compared FV cases, i.e., μFV(a) and μFV(b), respectively, are volume optimized.

Equations (51)

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

δ=λf/H=λF#sys.
V#=2πdNA/λ,
F#sys=fH=2fD=2F#,
δFIa=2λF#.
N=H2δFIa=D4λF#.
VMFIa=4D2f=28N3/2 δFIa3F#,
VMFIa=211F#4N3/2λ3=211F#4N3/2λ3.
RMFIa=L/D=4F#.
δFIb=δFIbcos θ=2λF#cos3 θ,
1cos2 θ=4F#2+14F#2.
N=H2δFIb=D cos3 θ4λF#.
VMFIb=4D2f=28F#4cos9 θN3/2 λ3=28F#41+14F#29/2N3/2 λ3.
1cos2 η=2F#2+N2F#2.
d=Δdβ=2λF#β cos3 η,
1cos2 η=2F#2+Nβ+122F#2,
VμFVa=4D2f=4fdβ+1N2,
VμFVa=25β+12F#4β32F#2+Nβ+122F#29/2Nλ3,
RμFVa=LD=4N F#.
VμFIa=25β+12F#4β3 Nλ3,
RμFIa=4N F#,
δFVb=δFVbcos η=2λF#cos3 η.
d=2δFVb=DN.
VμFVb=4D2f=28F#4cos9 ηNλ3=28F#42F#2+N2F#29/2Nλ3.
VμFIb=28F#4Nλ3.
w=γλ,
VGI=Nγλ2l,
a=wcos α.
Δl=wsin α.
VGV1=2wNa7N-8Δl/2=2N7N-8γλ3sin 2α.
Δl=2R sin α.
VGV2=4wNa log2 NΔl=8Nlog2 Nγλ2R tan α.
VGV=VGV1+VGV2.
N=2Nk+3,  k=1, 3, 5, .
VMFIaVMFIb=231+14F#2-9/2.
VμFIa=25F#+12F#Nλ3.
VμFIaVμFIb=F#+1223F#3,
VMFIaVμFIa=26F#3NF#+12,
VMFIbVμFIb=1+14F#29/2N,
VμFVF#=0,
VμFVβ=0,
F#μFVaopt=54NFVa1/2β+1,
β=1,
F#μFVbopt=54NFVb1/2.
VμFVaopt=2102959/2N3λ3,
VμFVbopt=52959/2N3λ3.
VMFIbVμFVb=NFIb3/2NFVbF#FIbF#FVb41+14F#FIb29/22F#FVb2+N[2F#FVb]29/2.
VMFIa|F#FVaopt=5227N7/2λ3,
VMFIb|F#FVbopt=525N+15N9/2N7/2λ3.
dVGVdα=0.
sin2 α=7N-88k log2 N+27N-8,
VGIopt=2Nγλ37N-88k log2 N+7N-81/2.

Metrics