Abstract

The fundamental reasons that determine the tolerance of free-space optical interconnect systems to misalignment are considered. By evaluation of the overlap of single-mode optical beams in the presence of misalignment it possible to determine an optimum beam configuration. It is shown that for any level of misalignment there is an optimum beam diameter that maximizes the coupling of light through the system. Many interconnect systems are not single mode throughout, so the analysis is extended to cover multimode systems. It is shown that, in principle, any level of misalignment can be accommodated by use of multimode beams, although at the cost of reduced channel density. It is shown that the presence of misalignment will mean that the number of channels that can be supported by an interconnect reduces with the length of the interconnect. As possible candidates for passively aligned systems, three example optical systems are analyzed by use of the methods developed.

© 1999 Optical Society of America

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References

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  1. F. A. P. Tooley, A. Z. Shang, B. Robertson, “Alignment tolerant smart pixels,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 55–56.
  2. G. C. Boisset, B. Robertson, H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
    [CrossRef]
  3. B. Robertson, “Design of a compact alignment tolerant optical interconnect for photonic backplane applications,” in Proceedings of the Fourth International Conference on Massively Parallel Processing Using Optical Interconnections (catalog no. 97TB100152), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 68–77.
    [CrossRef]
  4. S. Patra, M. Jian, V. Ozguz, S. H. Lee, “Alignment issues in packaging for free-space optical interconnects,” Opt. Eng. 33, 1561–1570 (1994).
    [CrossRef]
  5. D. Zaleta, S. Patra, V. Ozguz, M. Jian, S. H. Lee, “Tolerancing of board-level free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996).
    [CrossRef] [PubMed]
  6. D. A. B. Miller, “Physical reasons for optical interconnection,” Int. J. Optoelectron. 11, 155–168 (1997).
  7. H. Kogelnick, “Coupling and conversion coefficients for optical modes,” in Proceedings of the Symposium on Quasi-Optics, J. Fox, ed. (Polytechnic, Brooklyn, N.Y., 1964), Vol. 14, pp. 333–347.
  8. W. Smith, “Optics in practice,” in Modern Optical Engineering: the Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990), pp. 482–484.
  9. H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
    [CrossRef]
  10. A. E. Siegman, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
    [CrossRef]
  11. A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
    [CrossRef]
  12. A. V. Krishnamoorthy, D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21 st century: a technology roadmap,” IEEE J. Select. Topics Quantum Electron. 2, 55–76 (1996).
    [CrossRef]
  13. D. A. B. Miller, H. M. Ozaktas, “Limit to the bit-rate capacity of electrical interconnects from the aspect ratio of the system architecture,” J. Parallel Distribut. Comput. 41, 42–52 (1997).
    [CrossRef]
  14. J. Jahns, “Planar packaging of free–space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
    [CrossRef]
  15. J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
    [CrossRef]
  16. C. P. Barrett, P. Blair, G. S. Buller, D. T. Neilson, B. Robertson, E. C. Smith, M. R. Taghizadeh, A. C. Walker, “Components for implementation of free-space optical crossbars,” Appl. Opt. 35, 6934–6944 (1996).
    [CrossRef] [PubMed]
  17. D. J. Reiley, J. M. Sasian, “Optical design of a free-space photonics switching system,” Appl. Opt. 35, 6934–6944 (1996).
  18. D. T. Neilson, S. M. Prince, D. A. Baillie, F. A. P. Tooley, “Optical design of a 1024-channel free-space sorting demonstrator,” Appl. Opt. 36, 9243–9252 (1997).
    [CrossRef]
  19. D. J. Goodwill, H. S. Hinton, “Optical interconnect module extensible to 10,000 parallel channels for a smart-pixel optical backplane,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 61–62.

1997 (4)

D. A. B. Miller, “Physical reasons for optical interconnection,” Int. J. Optoelectron. 11, 155–168 (1997).

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

D. A. B. Miller, H. M. Ozaktas, “Limit to the bit-rate capacity of electrical interconnects from the aspect ratio of the system architecture,” J. Parallel Distribut. Comput. 41, 42–52 (1997).
[CrossRef]

D. T. Neilson, S. M. Prince, D. A. Baillie, F. A. P. Tooley, “Optical design of a 1024-channel free-space sorting demonstrator,” Appl. Opt. 36, 9243–9252 (1997).
[CrossRef]

1996 (4)

1995 (1)

G. C. Boisset, B. Robertson, H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

1994 (2)

S. Patra, M. Jian, V. Ozguz, S. H. Lee, “Alignment issues in packaging for free-space optical interconnects,” Opt. Eng. 33, 1561–1570 (1994).
[CrossRef]

J. Jahns, “Planar packaging of free–space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

1993 (2)

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

A. E. Siegman, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

1989 (1)

H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
[CrossRef]

Amitay, N.

H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
[CrossRef]

Baillie, D. A.

Barrett, C. P.

Benner, A. F.

H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
[CrossRef]

Blair, P.

Boisset, G. C.

G. C. Boisset, B. Robertson, H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

Bucholz, B.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Buller, G. S.

Chirovsky, L. M. F.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Crisci, R. J.

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

Cunningham, J. E.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Goodwill, D. J.

D. J. Goodwill, H. S. Hinton, “Optical interconnect module extensible to 10,000 parallel channels for a smart-pixel optical backplane,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 61–62.

Goossen, K. W.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Hinton, H. S.

G. C. Boisset, B. Robertson, H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

D. J. Goodwill, H. S. Hinton, “Optical interconnect module extensible to 10,000 parallel channels for a smart-pixel optical backplane,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 61–62.

Hui, S. P.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Jahns, J.

J. Jahns, “Planar packaging of free–space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

Jan, W. Y.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Jian, M.

D. Zaleta, S. Patra, V. Ozguz, M. Jian, S. H. Lee, “Tolerancing of board-level free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996).
[CrossRef] [PubMed]

S. Patra, M. Jian, V. Ozguz, S. H. Lee, “Alignment issues in packaging for free-space optical interconnects,” Opt. Eng. 33, 1561–1570 (1994).
[CrossRef]

Kogelnick, H.

H. Kogelnick, “Coupling and conversion coefficients for optical modes,” in Proceedings of the Symposium on Quasi-Optics, J. Fox, ed. (Polytechnic, Brooklyn, N.Y., 1964), Vol. 14, pp. 333–347.

Krishnamoorthy, A. V.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

A. V. Krishnamoorthy, D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21 st century: a technology roadmap,” IEEE J. Select. Topics Quantum Electron. 2, 55–76 (1996).
[CrossRef]

Lee, S. H.

D. Zaleta, S. Patra, V. Ozguz, M. Jian, S. H. Lee, “Tolerancing of board-level free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996).
[CrossRef] [PubMed]

S. Patra, M. Jian, V. Ozguz, S. H. Lee, “Alignment issues in packaging for free-space optical interconnects,” Opt. Eng. 33, 1561–1570 (1994).
[CrossRef]

Leibenguth, R. E.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Lentine, A. L.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

McCormick, F. B.

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

Mersereau, K. O.

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, H. M. Ozaktas, “Limit to the bit-rate capacity of electrical interconnects from the aspect ratio of the system architecture,” J. Parallel Distribut. Comput. 41, 42–52 (1997).
[CrossRef]

D. A. B. Miller, “Physical reasons for optical interconnection,” Int. J. Optoelectron. 11, 155–168 (1997).

A. V. Krishnamoorthy, D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21 st century: a technology roadmap,” IEEE J. Select. Topics Quantum Electron. 2, 55–76 (1996).
[CrossRef]

Morrison, R. L.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Neilson, D. T.

Novotny, R. A.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Ozaktas, H. M.

D. A. B. Miller, H. M. Ozaktas, “Limit to the bit-rate capacity of electrical interconnects from the aspect ratio of the system architecture,” J. Parallel Distribut. Comput. 41, 42–52 (1997).
[CrossRef]

Ozguz, V.

D. Zaleta, S. Patra, V. Ozguz, M. Jian, S. H. Lee, “Tolerancing of board-level free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996).
[CrossRef] [PubMed]

S. Patra, M. Jian, V. Ozguz, S. H. Lee, “Alignment issues in packaging for free-space optical interconnects,” Opt. Eng. 33, 1561–1570 (1994).
[CrossRef]

Patra, S.

D. Zaleta, S. Patra, V. Ozguz, M. Jian, S. H. Lee, “Tolerancing of board-level free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996).
[CrossRef] [PubMed]

S. Patra, M. Jian, V. Ozguz, S. H. Lee, “Alignment issues in packaging for free-space optical interconnects,” Opt. Eng. 33, 1561–1570 (1994).
[CrossRef]

Presby, H. M.

H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
[CrossRef]

Prince, S. M.

Reiley, D. J.

Robertson, B.

C. P. Barrett, P. Blair, G. S. Buller, D. T. Neilson, B. Robertson, E. C. Smith, M. R. Taghizadeh, A. C. Walker, “Components for implementation of free-space optical crossbars,” Appl. Opt. 35, 6934–6944 (1996).
[CrossRef] [PubMed]

G. C. Boisset, B. Robertson, H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

F. A. P. Tooley, A. Z. Shang, B. Robertson, “Alignment tolerant smart pixels,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 55–56.

B. Robertson, “Design of a compact alignment tolerant optical interconnect for photonic backplane applications,” in Proceedings of the Fourth International Conference on Massively Parallel Processing Using Optical Interconnections (catalog no. 97TB100152), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 68–77.
[CrossRef]

Sasian, J. M.

D. J. Reiley, J. M. Sasian, “Optical design of a free-space photonics switching system,” Appl. Opt. 35, 6934–6944 (1996).

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

Scotti, R.

H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
[CrossRef]

Shang, A. Z.

F. A. P. Tooley, A. Z. Shang, B. Robertson, “Alignment tolerant smart pixels,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 55–56.

Siegman, A. E.

A. E. Siegman, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Smith, E. C.

Smith, W.

W. Smith, “Optics in practice,” in Modern Optical Engineering: the Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990), pp. 482–484.

Stawicki, R. P.

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

Taghizadeh, M. R.

Tooley, F. A. P.

D. T. Neilson, S. M. Prince, D. A. Baillie, F. A. P. Tooley, “Optical design of a 1024-channel free-space sorting demonstrator,” Appl. Opt. 36, 9243–9252 (1997).
[CrossRef]

F. A. P. Tooley, A. Z. Shang, B. Robertson, “Alignment tolerant smart pixels,” in Advanced Applications of Lasers in Materials Processing/Broadband Optical Networks/Enabling Technologies and Applications/Smart Pixels/Optical MEM’s and Their Applications: IEEE/LEOS 1996 Summer Topical Meetings (catalog no. 96TH8164) (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 55–56.

Tseng, B. T.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Walker, A. C.

Walker, J. A.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Webb, R.

J. M. Sasian, F. B. McCormick, R. Webb, R. J. Crisci, K. O. Mersereau, R. P. Stawicki, “Design, assembly, and testing of an objective lens for a free-space photonic switching system,” Opt. Eng. 32, 1871–1878 (1993).
[CrossRef]

Woodward, T. K.

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

Zaleta, D.

Appl. Opt. (4)

Electron. Lett. (1)

A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, T. K. Woodward, A. V. Krishnamoorthy, S. P. Hui, B. T. Tseng, R. E. Leibenguth, L. M. F. Chirovsky, R. A. Novotny, B. Bucholz, R. L. Morrison, “Optoelectronic VLSI switching chip with greater than 1 terabit per second potential I/O bandwidth,” Electron. Lett. 33, 894–895 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. E. Siegman, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

IEEE J. Select. Topics Quantum Electron. (1)

A. V. Krishnamoorthy, D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21 st century: a technology roadmap,” IEEE J. Select. Topics Quantum Electron. 2, 55–76 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. C. Boisset, B. Robertson, H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

Int. J. Optoelectron. (1)

D. A. B. Miller, “Physical reasons for optical interconnection,” Int. J. Optoelectron. 11, 155–168 (1997).

J. Lightwave Technol. (1)

H. M. Presby, N. Amitay, R. Scotti, A. F. Benner, “Laser-to-fiber coupling via optical fiber up-tapers,” J. Lightwave Technol. 7, 274–278 (1989).
[CrossRef]

J. Parallel Distribut. Comput. (1)

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Figures (9)

Fig. 1
Fig. 1

Illustration of the lateral δx and the angular δθ misalignment of modes.

Fig. 2
Fig. 2

Single-mode to single-mode coupling as a function of the beam size for different levels of misalignment. Shown are results for a λ = 1 µm beam with angular misalignments of 1, 2, 4, 8, 16, and 32 arc min and corresponding lateral misalignments (in micrometers).

Fig. 3
Fig. 3

Misalignment of 16-µm/arc min for different mode numbers. Selecting a coupling level makes it possible to find a matching beam size and mode number. For the 90% coupling shown the beam size is W = 70 µm and M 2 = 4.4.

Fig. 4
Fig. 4

Graph illustrating that the same coupling efficiency can be achieved for different levels of misalignment by means of increasing the beam size and the degree to which the beam is multimode: (a) δx = 8 µm, δθ = 8 arc min, and M 2 = 1. (b) δx = 16 µm, δθ = 16 arc min, and M 2 = 4. (c) δx = 32 µm, δθ = 32 arc min, and M 2 = 16. (d) δx = 64 µm, δθ = 64 arc min, and M 2 = 64.

Fig. 5
Fig. 5

Channel density possible in channels (Ch) per millimeter squared as a function of the alignment error in micrometers and minutes of arc.

Fig. 6
Fig. 6

Types of optical systems that are considered as examples: (a) a conventional lens, (b) a minilens, (c) a microlens.

Fig. 7
Fig. 7

Conventional lens system with f = 30 mm and an f/4 lens system. Contour plots of the coupling efficiency as a function of the lateral δx and the angular δθ misalignment for (a) a single-mode beam with M 2 = 1 and W = 2.52 µm and (b) a multimode beam with M 2 = 4 and W = 10.08 µm. (c) Fourier plane results for M 2 = 1 and W = 3.75 mm. (d) Fourier plane results for M 2 = 4 and W = 3.75 mm.

Fig. 8
Fig. 8

Minilens system with f = 8.5 mm, f/12.23, and λ = 0.85 µm. Contour plots of the coupling efficiency as a function of the lateral δx and the angular δθ misalignment for (a) a single-mode beam with M 2 = 1 and W = 6.55 µm, (b) a single-mode beam on the Fourier plane with M 2 = 1 and W = 350 µm, (c) a multimode beam with M 2= 3 and W = 19.65 µm, (d) a multimode beam on the Fourier plane with M 2 = 3 and W = 350 µm.

Fig. 9
Fig. 9

Gaussian beam relay microlens system. Contour plots of the coupling efficiency as a function of the lateral δx and the angular δθ misalignment for (a) a single-mode beam with M 2 = 1 and W = 25.3 µm and (b) a multimode beam with M 2 = 3.07 and W = 44.2 µm.

Equations (17)

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η=-- ϕψ*dxdy2-- ϕϕ*dxdy -- ψψ*dxdy.
ϕ=exp-x2+y2W2.
ψδx=exp-x+δx2+y2W2.
ηδx=exp-δx2W2.
ψδθ=exp-x2+y2W2expx 2πiλtan δθ.
ηδθ=exp-W2π2λ2tan δθ2.
ηδθ,δx=exp-W2π2λ2tan δθ2exp-δx2W2.
WηMAX=λδxπ tan δθ1/2.
ηδθ,δxmax=exp-2πδx tan δθλ.
δzη=90%=2.095W2λ.
WEff=WM2=W1+2 δxW21/2.
ηδθ,δx=exp-W2π2M2λ2tan δθ2exp-δx2W2.
WηMAX=M2λδxπ tan δθ1/2.
ηδθ,δxmax=exp-2πδx tan δθM2λ.
B  Al2.
B  Al.
W=0.64λf/#.

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