Abstract

We investigate the design of free-space optical interconnects (FSOIs) based on arrays of vertical-cavity surface-emitting lasers (VCSELs), microlenses, and photodetectors. We explain the effect of the modal structure of a multimode VCSEL beam on the performance of a FSOI with microchannel architecture. A Gaussian-beam diffraction model is used in combination with the experimentally obtained spectrally resolved VCSEL beam profiles to determine the optical channel crosstalk and the signal-to-noise ratio (SNR) in the system. The dependence of the SNR on the feature parameters of a FSOI is investigated. We found that the presence of higher-order modes reduces the SNR and the maximum feasible interconnect distance. We also found that the positioning of a VCSEL array relative to the transmitter microlens has a significant impact on the SNR and the maximum feasible interconnect distance. Our analysis shows that the departure from the traditional confocal system yields several advantages including the extended interconnect distance and/or improved SNR. The results show that FSOIs based on multimode VCSELs can be efficiently utilized in both chip-level and board-level interconnects.

© 2002 Optical Society of America

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  23. V. E. Boros, A. D. Rakić, M. L. Majewski, “Measurement automation for characterising VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 392–395.
  24. R. Michalzik, K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
    [CrossRef]
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1999 (1)

R. Wang, A. D. Rakić, M. L. Majewski, “Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers,” Opt. Commun. 167, 261–271 (1999).
[CrossRef]

1998 (3)

1997 (1)

1996 (3)

1995 (2)

T. Sakano, T. Matsumoto, K. Noguchi, “Three-dimensional board-to-board free-space optical interconnection and their application to the prototype multiprocessor system: Cosine-III,” Appl. Opt. 34, 1815–1822 (1995).
[CrossRef] [PubMed]

R. Michalzik, K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

1994 (1)

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

1992 (3)

1991 (1)

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

1984 (1)

J. W. Goodman, F. J. Leonberger, S. C. Kung, R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1982 (1)

Asom, M. T.

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. J. Leonberger, S. C. Kung, R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Ayliffe, M. H.

Belland, P.

Bennion, I.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Bertilsson, K.

Boisset, G. C.

Borghi, R.

Boros, V. B.

A. D. Rakić, V. B. Boros, M. I. Cohen, M. L. Majewski, “Cooperatively frequency-locked multimode operation in proton implanted VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 116–119.

Boros, V. E.

V. E. Boros, A. D. Rakić, M. L. Majewski, “Measurement automation for characterising VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 392–395.

Bryan, R. P.

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

Catchmark, J. M.

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

Chen, R. T.

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

Christomodulides, D. N.

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

Cloonan, T. J.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Cohen, M. I.

A. D. Rakić, V. B. Boros, M. I. Cohen, M. L. Majewski, “Cooperatively frequency-locked multimode operation in proton implanted VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 116–119.

Coldren, L. A.

E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811–2821 (1998).
[CrossRef]

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Craft, N. C.

Crenn, J. P.

Ebeling, K. J.

R. Michalzik, K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

Feldblum, A. Y.

N. C. Craft, A. Y. Feldblum, “Optical interconnects based on arrays of surface-emitting lasers and lenslets,” Appl. Opt. 31, 1735–1739 (1992).
[CrossRef] [PubMed]

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Fu, W. S.

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

Garat, L.

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

Gerold, D.

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, (IEEE Press/Chapman & Hall Publishers Series on Microwave Technology, New York, 1998), Chap. 2.
[CrossRef]

Goodfellow, R. C.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, S. C. Kung, R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Goodwin, M. J.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Guth, G. D.

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

Hinton, H. S.

Hsiao, W.

Jayaraman, V.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. A. White, Fundamentals of Optics, (McGraw-Hill, Inc., New York, 1976), Chap. 5.

Jewell, J. L.

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

Kabal, D.

Kearley, M. Q.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Kim, N. H.

Kirkby, C. J. G.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Kostuk, R. K.

Kung, S. C.

J. W. Goodman, F. J. Leonberger, S. C. Kung, R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Kurokawa, T.

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, S. C. Kung, R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Li, M. M.

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

Liu, Y. S.

Louderback, D. A.

Majewski, M. L.

R. Wang, A. D. Rakić, M. L. Majewski, “Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers,” Opt. Commun. 167, 261–271 (1999).
[CrossRef]

V. E. Boros, A. D. Rakić, M. L. Majewski, “Measurement automation for characterising VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 392–395.

A. D. Rakić, V. B. Boros, M. I. Cohen, M. L. Majewski, “Cooperatively frequency-locked multimode operation in proton implanted VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 116–119.

Matso, S.

Matsumoto, T.

McCormick, F. B.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Mersereau, K. O.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Michalzik, R.

R. Michalzik, K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

Mondry, M.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Morgan, R. A.

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

Morris, R. C.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Moseley, A. J.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Nakahara, T.

Neifeld, M. A.

Noguchi, K.

Ohiso, Y.

Olbright, G. R.

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

Otazo, M. R.

Pavlasek, D.

Peters, F. H.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Peters, M. G.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Plant, D. V.

Quinn, W. E.

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

Rakic, A. D.

R. Wang, A. D. Rakić, M. L. Majewski, “Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers,” Opt. Commun. 167, 261–271 (1999).
[CrossRef]

V. E. Boros, A. D. Rakić, M. L. Majewski, “Measurement automation for characterising VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 392–395.

A. D. Rakić, V. B. Boros, M. I. Cohen, M. L. Majewski, “Cooperatively frequency-locked multimode operation in proton implanted VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 116–119.

Robertson, B.

Robertson, W. M.

Robinson, G. D.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Rogers, L. E.

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

Sakano, T.

Santarsiero, M.

Sasian, J. M.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Shang, A. Z.

Siegmann, A. E.

A. E. Siegmann, Lasers, (University Science, Mill Valley, Calif., 1986), Chap. 17.

Simmons, J.

Song, K.

Strzelecka, E. M.

E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811–2821 (1998).
[CrossRef]

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Swirhun, S. E.

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

Tang, S.

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

Tateno, K.

Thibeault, B. J.

E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811–2821 (1998).
[CrossRef]

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Thompson, D. A.

Thompson, G. B.

E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811–2821 (1998).
[CrossRef]

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

Thompson, J.

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

Tooley, F. A. P.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Tsuda, H.

Tu, K.

Wakatsuki, A.

Wang, R.

R. Wang, A. D. Rakić, M. L. Majewski, “Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers,” Opt. Commun. 167, 261–271 (1999).
[CrossRef]

White, H. A.

F. A. Jenkins, H. A. White, Fundamentals of Optics, (McGraw-Hill, Inc., New York, 1976), Chap. 5.

Yeh, J.

Appl. Opt. (9)

T. Sakano, T. Matsumoto, K. Noguchi, “Three-dimensional board-to-board free-space optical interconnection and their application to the prototype multiprocessor system: Cosine-III,” Appl. Opt. 34, 1815–1822 (1995).
[CrossRef] [PubMed]

D. V. Plant, B. Robertson, H. S. Hinton, M. H. Ayliffe, G. C. Boisset, W. Hsiao, D. Kabal, N. H. Kim, Y. S. Liu, M. R. Otazo, D. Pavlasek, A. Z. Shang, J. Simmons, K. Song, D. A. Thompson, W. M. Robertson, “4 × 4 VCSEL and metal-semiconductor-metal optical backplane demonstrator system,” Appl. Opt. 35, 6365–6368 (1996).
[CrossRef] [PubMed]

T. Kurokawa, S. Matso, T. Nakahara, K. Tateno, Y. Ohiso, A. Wakatsuki, H. Tsuda, “Design approaches for VCSELs and VCSEL-based smart pixels toward parallel optoelectronic processing system,” Appl. Opt. 37, 194–204 (1998).
[CrossRef]

N. C. Craft, A. Y. Feldblum, “Optical interconnects based on arrays of surface-emitting lasers and lenslets,” Appl. Opt. 31, 1735–1739 (1992).
[CrossRef] [PubMed]

J. Yeh, R. K. Kostuk, K. Tu, “Hybrid free-space optical bus system for board-to-board interconnections,” Appl. Opt. 35, 6354–6364 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, R. K. Kostuk, “Error correction for free-space optical interconnects: space-time resource optimization,” Appl. Opt. 37, 296–307 (1998).
[CrossRef]

R. K. Kostuk, “Simulation of board-level free-space optical interconnects for electronic processing,” Appl. Opt. 31, 2438–2445 (1992).
[CrossRef] [PubMed]

E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811–2821 (1998).
[CrossRef]

P. Belland, J. P. Crenn, “Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture,” Appl. Opt. 21, 522–527 (1982).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

J. M. Catchmark, L. E. Rogers, R. A. Morgan, M. T. Asom, G. D. Guth, D. N. Christomodulides, “Optical characteristics of multi-transverse mode 2-D vertical-cavity top surface-emitting laser arrays,” IEEE J. Quantum Electron. 32, 986–995 (1996).
[CrossRef]

R. Michalzik, K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

J. Lightwave Technol. (2)

M. J. Goodwin, A. J. Moseley, M. Q. Kearley, R. C. Morris, C. J. G. Kirkby, J. Thompson, R. C. Goodfellow, I. Bennion, “Optoelectronic component arrays for optical interconnection of circuits and subsystems,” J. Lightwave Technol. 9, 1639–1644 (1991).
[CrossRef]

S. Tang, R. T. Chen, L. Garat, D. Gerold, M. M. Li, “Design limitation of highly parallel free-space optical interconnects based on arrays of VCSEL laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
[CrossRef]

Opt. Commun. (1)

R. Wang, A. D. Rakić, M. L. Majewski, “Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers,” Opt. Commun. 167, 261–271 (1999).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, A. Y. Feldblum, “Optical interconnection using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
[CrossRef]

Proc. IEEE (1)

J. W. Goodman, F. J. Leonberger, S. C. Kung, R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Other (8)

A. D. Rakić, V. B. Boros, M. I. Cohen, M. L. Majewski, “Cooperatively frequency-locked multimode operation in proton implanted VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 116–119.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, L. A. Coldren, “Monolithic integration of refractive lenses with vertical-cavity lasers and detectors for optical interconnections,” in Optoelectronic Packaging, M. R. Feldman, Y.-C. Lee, eds., Proc. SPIE2691, 43–54 (1996).
[CrossRef]

S. E. Swirhun, R. P. Bryan, W. S. Fu, W. E. Quinn, J. L. Jewell, G. R. Olbright, “Commercial manufacturing of vertical-cavity surface-emitting laser arrays,” in Vertical-Cavity Surface-Emitting Laser Arrays, J. L. Jewell, ed., Proc. SPIE2147, 74–84 (1994).
[CrossRef]

V. E. Boros, A. D. Rakić, M. L. Majewski, “Measurement automation for characterising VCSELs,” in Conference on Optoelectronic and Microelectronic Materials and Devices COMMAD’98 (IEEE Press, New York, 1999), pp. 392–395.

A. E. Siegmann, Lasers, (University Science, Mill Valley, Calif., 1986), Chap. 17.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, (IEEE Press/Chapman & Hall Publishers Series on Microwave Technology, New York, 1998), Chap. 2.
[CrossRef]

F. A. Jenkins, H. A. White, Fundamentals of Optics, (McGraw-Hill, Inc., New York, 1976), Chap. 5.

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Figures (12)

Fig. 1
Fig. 1

Schematic of (a) free-space optical interconnect and (b) Gaussian diffraction model.

Fig. 2
Fig. 2

Structure of (a) VCSEL array and (b) Rx lens array.

Fig. 3
Fig. 3

Lasing spectra for various injection currents to a VCSEL.

Fig. 4
Fig. 4

Optical power for different modes of a multi-transverse mode beam versus the injection current.

Fig. 5
Fig. 5

Contribution of different modes to the total output power of the VCSEL.

Fig. 6
Fig. 6

Dependence of SNR on interconnect distance L. ω0 = 2.25 µm, Δ = 0.25 mm, D = Δ, d 1 = 1.70 mm.

Fig. 7
Fig. 7

Dependence of SNR on channel spacing. ω0 = 2.25 µm, D = Δ.

Fig. 8
Fig. 8

Dependence of SNR on fill factor β. ω0 = 2.25 µm, Δ = 0.25 mm, D = βΔ.

Fig. 9
Fig. 9

Dependence of beam spot ω2 on ratio d 1/f. ω0 = 2.25 µm, Δ = 0.25 mm, D = Δ, d 1 = 1.70 mm.

Fig. 10
Fig. 10

Dependence of SNR on ratio d 1/f. ω0 = 2.25 µm, Δ = 0.25 mm, D = Δ, d 1 = 1.70 mm.

Fig. 11
Fig. 11

Dependence of maximum interconnect distance on ratio d 1/f. ω0 = 2.25 µm, Δ = 0.25 mm, D = Δ, d 1 = 1.70 mm.

Fig. 12
Fig. 12

Algorithm for the design of FSOIs. For detailed description of the procedure refer to Section 5 steps (a) to (d).

Equations (13)

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SNR=10 log10P0SP0N+NEPBdB,
f=nn-1 R1,
ω1=ω01+d1/ZR21/2,
ω10=ω01-d1/f2+ZR/f21/2,
d2=-d1/n1-d1/f-ZR2/f1-d1/f2+ZR/f2.
ω2=ω101+d3/ZR21/2,
ω20=ω101-nd3/f2+nZR/f21/2,
d4=-nd31-nd3/f-nZR2/f1-nd3/f2+nZR/f2.
Ir, θ, d3=p,m CpmIpmr, θ, d3 =p,m Cpm4p!πω22p+m!1+δ0m2rω22m×Lpm2r2ω222 exp-2r2ω22cos2mθ,
S= Ω0 Ir, θ, d3rdrdθ.
N=2 Ω1+Ω2+Ω3+Ω4 Ir, θ, d3rdrdθ.
d2=n+1f/2n+f2/2nZR.
d1ZRD218ω02-11/2.

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