Abstract

A free-space optical bus system is described for board-to-board interconnections at the backplane level. The system uses active optoelectronic modules as the interface between the circuit boards and the electrical backplane. Substrate-mode holograms are used to implement signal broadcast operations between boards, and each board on the backplane shares common free-space channels for transmitting and receiving signals. System-design considerations are given, and the potential performance of the optical bus system is evaluated. An experimental demonstration is also presented for the signal broadcast operation through cascaded substrate-mode holograms at a data rate of 622 Mb/s.

© 1996 Optical Society of America

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References

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    [CrossRef]
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  23. M. Kato, Y.-T. Huang, R. K. Kostuk, “Multiplexed substrate-mode holograms,” J. Opt. Soc. Am. A 7, 1441–1447 (1990).
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  30. K.-Y. Tu, J.-H. Yeh, R. K. Kostuk, “Receiver considerations for free-space optical clock distribution systems,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. SPIE2153, 86–93 (1994).
  31. J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “Board-level H-tree optical clock distribution with substrate-mode holograms,” J. Lightwave Technol. 13, 1566–1578 (1995).
    [CrossRef]
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    [CrossRef]
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1995

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

S. H. Song, E. H. Lee, “Focusing-grating-coupler arrays for uniform and efficient signal distribution in a backboard optical interconnect,” Appl. Opt. 34, 5913–5919 (1995).
[CrossRef] [PubMed]

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multiprocessor board-to-board optoelectronic interconnects,” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

J.-H. Yeh, R. K. Kostuk, “Substrate-mode holograms used in optical interconnects: design issues,” Appl. Opt. 34, 3152–3164 (1995).
[CrossRef] [PubMed]

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “Board-level H-tree optical clock distribution with substrate-mode holograms,” J. Lightwave Technol. 13, 1566–1578 (1995).
[CrossRef]

1993

1992

W. S. Lee, D. A. H. Spear, A. D. Smith, S. A. Wheeler, S. W. Bland, “Monolithic eight-channel photoreceiver array OEICs for HDWDM applications at 1.55 mm,” Electron. Lett. 28, 612–614 (1992).
[CrossRef]

F. MacKenzie, T. G. Hodgkinson, S. A. Cassidy, P. Healy, “Optical interconnect based on a fiber bus,” Opt. Quantum Electron. 24, 491–504 (1992).
[CrossRef]

1991

1990

1989

F. Sauer, “Fabrication of diffractive–reflective optical interconnects for infrared operation based on total internal reflection,” Appl. Opt. 28, 386–388 (1989).
[CrossRef] [PubMed]

C. H. Henry, G. E. Blonder, R. F. Kazarinov, “Glass waveguides on silicon for hybrid optical packaging,” IEEE J. Lightwave Technol. 7, 1530–1539 (1989).
[CrossRef]

1975

1969

H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 58, 2909–2947 (1969).

Baets, R.

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

Balavkrishnan, R. V.

R. V. Balavkrishnan, “Transceiver technology and design,” in Digital Bus Handbook, J. D. Giacomo, ed. (McGraw-Hill, New York, 1990), Chap. 14, pp. 14.1–14.41.

Black, J.

J. Black, The System Engineer's Handbook: A Guide to Building VMEbus and VXIbus Systems (Academic, New York, 1992).

Bland, S. W.

W. S. Lee, D. A. H. Spear, A. D. Smith, S. A. Wheeler, S. W. Bland, “Monolithic eight-channel photoreceiver array OEICs for HDWDM applications at 1.55 mm,” Electron. Lett. 28, 612–614 (1992).
[CrossRef]

Blondelle, J.

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

Blonder, G. E.

C. H. Henry, G. E. Blonder, R. F. Kazarinov, “Glass waveguides on silicon for hybrid optical packaging,” IEEE J. Lightwave Technol. 7, 1530–1539 (1989).
[CrossRef]

Campbell, E. W.

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin-coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. SPIE1914, 91–100 (1993).

Case, S. K.

Cassidy, S. A.

F. MacKenzie, T. G. Hodgkinson, S. A. Cassidy, P. Healy, “Optical interconnect based on a fiber bus,” Opt. Quantum Electron. 24, 491–504 (1992).
[CrossRef]

Chen, E.

R. C. Kim, E. Chen, F. Lin, “An optical holographic back-plane interconnect system,” IEEE J. Lightwave Technol. 9, 1650–1656 (1990).
[CrossRef]

Chen, R. T.

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multiprocessor board-to-board optoelectronic interconnects,” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, D. Plant, H. Fetterman, “High-speed board-to-board optical interconnection,” in Photopolymer Device Physics, Chemistry, and Applications II, R. A. Lessard, ed., Proc. SPIE1559, 110–117 (1991).

De Dobbelaere, P.

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

Demeester, P.

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

Dhoedt, B.

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

Fetterman, H.

R. T. Chen, H. Lu, D. Robinson, D. Plant, H. Fetterman, “High-speed board-to-board optical interconnection,” in Photopolymer Device Physics, Chemistry, and Applications II, R. A. Lessard, ed., Proc. SPIE1559, 110–117 (1991).

Fink, M.

Giacomo, J. D.

J. D. Giacomo, “Limits of performance of backplane buses,” in Digital Bus Handbook, J. D. Giacomo, ed. (McGraw-Hill, New York, 1990), Chap. 18, pp. 18.1–18.23.

J. D. Giacomo, Digital Bus Handbook (McGraw-Hill, New York, 1990).

Hamanaka, K.

Haumann, H.-J.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Hawley, D.

D. Hawley, “Future bus,” in Digital Bus Handbook, J. D. Giacomo, ed. (McGraw-Hill, New York, 1990), Chap. 7 pp.7.1–7.39.

Healy, P.

F. MacKenzie, T. G. Hodgkinson, S. A. Cassidy, P. Healy, “Optical interconnect based on a fiber bus,” Opt. Quantum Electron. 24, 491–504 (1992).
[CrossRef]

Henry, C. H.

C. H. Henry, G. E. Blonder, R. F. Kazarinov, “Glass waveguides on silicon for hybrid optical packaging,” IEEE J. Lightwave Technol. 7, 1530–1539 (1989).
[CrossRef]

Hetherington, D.

Hodgkinson, T. G.

F. MacKenzie, T. G. Hodgkinson, S. A. Cassidy, P. Healy, “Optical interconnect based on a fiber bus,” Opt. Quantum Electron. 24, 491–504 (1992).
[CrossRef]

Huang, Y.-T.

Kato, M.

Kazarinov, R. F.

C. H. Henry, G. E. Blonder, R. F. Kazarinov, “Glass waveguides on silicon for hybrid optical packaging,” IEEE J. Lightwave Technol. 7, 1530–1539 (1989).
[CrossRef]

Kiefer, D. R.

D. R. Kiefer, V. W. Swanson, “Implementation of optical clock distribution in a supercomputer,” in Optical Computing, Vol.10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 260–262.

Kim, R. C.

R. C. Kim, E. Chen, F. Lin, “An optical holographic back-plane interconnect system,” IEEE J. Lightwave Technol. 9, 1650–1656 (1990).
[CrossRef]

Kim, T. J.

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin-coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. SPIE1914, 91–100 (1993).

Kobolla, H.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 58, 2909–2947 (1969).

Kostuk, R. K.

J.-H. Yeh, R. K. Kostuk, “Substrate-mode holograms used in optical interconnects: design issues,” Appl. Opt. 34, 3152–3164 (1995).
[CrossRef] [PubMed]

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “Board-level H-tree optical clock distribution with substrate-mode holograms,” J. Lightwave Technol. 13, 1566–1578 (1995).
[CrossRef]

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board-level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[CrossRef] [PubMed]

R. K. Kostuk, M. Kato, Y.-T. Huang, “Polarization properties of substrate-mode holographic interconnects,” Appl. Opt. 29, 3848–3854 (1990).
[CrossRef] [PubMed]

M. Kato, Y.-T. Huang, R. K. Kostuk, “Multiplexed substrate-mode holograms,” J. Opt. Soc. Am. A 7, 1441–1447 (1990).
[CrossRef]

R. K. Kostuk, Y.-T. Huang, D. Hetherington, M. Kato, “Reduced alignment and chromatic sensitivity of holographic optical interconnects with substrate-mode holograms,” Appl. Opt. 28, 4939–4944 (1990).
[CrossRef]

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin-coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. SPIE1914, 91–100 (1993).

K.-Y. Tu, J.-H. Yeh, R. K. Kostuk, “Receiver considerations for free-space optical clock distribution systems,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. SPIE2153, 86–93 (1994).

Lee, E. H.

Lee, W. S.

W. S. Lee, D. A. H. Spear, A. D. Smith, S. A. Wheeler, S. W. Bland, “Monolithic eight-channel photoreceiver array OEICs for HDWDM applications at 1.55 mm,” Electron. Lett. 28, 612–614 (1992).
[CrossRef]

Lin, F.

R. C. Kim, E. Chen, F. Lin, “An optical holographic back-plane interconnect system,” IEEE J. Lightwave Technol. 9, 1650–1656 (1990).
[CrossRef]

Lu, H.

R. T. Chen, H. Lu, D. Robinson, D. Plant, H. Fetterman, “High-speed board-to-board optical interconnection,” in Photopolymer Device Physics, Chemistry, and Applications II, R. A. Lessard, ed., Proc. SPIE1559, 110–117 (1991).

MacKenzie, F.

F. MacKenzie, T. G. Hodgkinson, S. A. Cassidy, P. Healy, “Optical interconnect based on a fiber bus,” Opt. Quantum Electron. 24, 491–504 (1992).
[CrossRef]

Matsumoto, T.

Natarajan, S.

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multiprocessor board-to-board optoelectronic interconnects,” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

Noguchi, K.

Plant, D.

R. T. Chen, H. Lu, D. Robinson, D. Plant, H. Fetterman, “High-speed board-to-board optical interconnection,” in Photopolymer Device Physics, Chemistry, and Applications II, R. A. Lessard, ed., Proc. SPIE1559, 110–117 (1991).

Robinson, D.

R. T. Chen, H. Lu, D. Robinson, D. Plant, H. Fetterman, “High-speed board-to-board optical interconnection,” in Photopolymer Device Physics, Chemistry, and Applications II, R. A. Lessard, ed., Proc. SPIE1559, 110–117 (1991).

Sakano, T.

Sauer, F.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

F. Sauer, “Fabrication of diffractive–reflective optical interconnects for infrared operation based on total internal reflection,” Appl. Opt. 28, 386–388 (1989).
[CrossRef] [PubMed]

Sawabe, T.

Schmidt, J.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Schwider, J.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Sebillotte, C.

C. Sebillotte, “Holographic optical backplane for boards interconnection,” in Microelectronic Interconnects and Packages: Optical and Electrical Technologies, G. Arjavalingam, J. Pazaris, eds., Proc. SPIE1389, 600–611 (1990).

Smith, A. D.

W. S. Lee, D. A. H. Spear, A. D. Smith, S. A. Wheeler, S. W. Bland, “Monolithic eight-channel photoreceiver array OEICs for HDWDM applications at 1.55 mm,” Electron. Lett. 28, 612–614 (1992).
[CrossRef]

Song, S. H.

Spear, D. A. H.

W. S. Lee, D. A. H. Spear, A. D. Smith, S. A. Wheeler, S. W. Bland, “Monolithic eight-channel photoreceiver array OEICs for HDWDM applications at 1.55 mm,” Electron. Lett. 28, 612–614 (1992).
[CrossRef]

Stork, W.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Streibl, N.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Swanson, V. W.

D. R. Kiefer, V. W. Swanson, “Implementation of optical clock distribution in a supercomputer,” in Optical Computing, Vol.10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 260–262.

Tu, K.-Y.

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “Board-level H-tree optical clock distribution with substrate-mode holograms,” J. Lightwave Technol. 13, 1566–1578 (1995).
[CrossRef]

K.-Y. Tu, J.-H. Yeh, R. K. Kostuk, “Receiver considerations for free-space optical clock distribution systems,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. SPIE2153, 86–93 (1994).

Van Daele, P.

B. Dhoedt, P. De Dobbelaere, J. Blondelle, P. Van Daele, P. Demeester, R. Baets, “Monolithic integration of diffractive lenses with LED arrays for a board-to-board free-space optical interconnect,” J. Lightwave Technol. 13, 1065–1073 (1995).
[CrossRef]

Volkel, R.

H.-J. Haumann, H. Kobolla, F. Sauer, J. Schmidt, J. Schwider, W. Stork, N. Streibl, R. Volkel, “Optoelectronic interconnection based on a light-guiding plate with holographic coupling elements,” Opt. Eng. 30, 1620–1623 (1991).
[CrossRef]

Wheeler, S. A.

W. S. Lee, D. A. H. Spear, A. D. Smith, S. A. Wheeler, S. W. Bland, “Monolithic eight-channel photoreceiver array OEICs for HDWDM applications at 1.55 mm,” Electron. Lett. 28, 612–614 (1992).
[CrossRef]

Yeh, J.-H.

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “Board-level H-tree optical clock distribution with substrate-mode holograms,” J. Lightwave Technol. 13, 1566–1578 (1995).
[CrossRef]

J.-H. Yeh, R. K. Kostuk, “Substrate-mode holograms used in optical interconnects: design issues,” Appl. Opt. 34, 3152–3164 (1995).
[CrossRef] [PubMed]

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board-level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[CrossRef] [PubMed]

K.-Y. Tu, J.-H. Yeh, R. K. Kostuk, “Receiver considerations for free-space optical clock distribution systems,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. SPIE2153, 86–93 (1994).

Zhao, C.

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multiprocessor board-to-board optoelectronic interconnects,” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

Appl. Opt.

T. Sakano, T. Matsumoto, K. Noguchi, T. Sawabe, “Design and performance of a multiprocessor system employing board-to-board free-space optical interconnections: COSINE-1,” Appl. Opt. 30, 2334–2343 (1991).
[CrossRef] [PubMed]

T. Sakano, K. Noguchi, T. Matsumoto, “Multiprocessor system using an automatically rearrangeable free-space multichannel optical switch: COSINE-II,” Appl. Opt. 32, 3690–3699 (1993).
[CrossRef] [PubMed]

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

S. H. Song, E. H. Lee, “Focusing-grating-coupler arrays for uniform and efficient signal distribution in a backboard optical interconnect,” Appl. Opt. 34, 5913–5919 (1995).
[CrossRef] [PubMed]

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board-level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[CrossRef] [PubMed]

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the hybrid free-space optical bus system for board-to-board interconnections. The OE modules replace passive connectors and are used as the interface between circuit boards and the conventional electrical backplane.

Fig. 2
Fig. 2

Basic SMH components used in the optical bus system: S0, S1, and S2 are single SMH's and M1 is a 1 × 2 multiplexed SMH. (a) An input–output coupler, (b) an M1 SMH direct-coupling-mode component, and (c) an M1 SMH cross-coupling-mode component. (d) The corresponding Bragg diagrams for SMH's S0 (S2), S1, and M1.

Fig. 3
Fig. 3

Implementation of the signal broadcast distribution with SMH components for signals transmitted from circuit boards (a) A, (b) B, and (c) C. O/E module, optoelectronic module.

Fig. 4
Fig. 4

Interconnect design of optical bus systems for (a) six boards (B1–B6) and (b) eight boards (B1–B8).

Fig. 5
Fig. 5

(a) Photograph of the experimental setup for the demonstration of the signal broadcast distribution with SMH components. (b) Received signal waveform (upper trace) with a data rate of 622 Mbits/s and the corresponding eye diagrams (lower trace).

Fig. 6
Fig. 6

Plots for the optical-link efficiencies ηAB (=ηBA), ηAC (=ηAD = ηBC = ηBD = ηCA = ηDA), ηCB (=ηDB), and ηCD (=ηDC), respectively, as functions of the refractive-index modulation (n 1 = n 2).

Fig. 7
Fig. 7

Value of M plotted as a function of the refractive-index modulation (n 1 = n 2). M is used to determine the merit of the optical-power-budget design.

Fig. 8
Fig. 8

Schematic diagram of a basic free-space board-to-board interconnect in the optical bus system. The lenses are used for collimating and focusing, and the SMH components are designed for signal broadcasting.

Fig. 9
Fig. 9

(a) Beam displacement Δs 1 caused by the angular misalignment Δθ between two OE modules with a separation distance of L. (b) The resultant beam displacement Δs 2 owing to Δθ and the wavelength variation Δλ for a signal beam propagating within the substrate.

Fig. 10
Fig. 10

Schematic diagram of the power loss and optical cross talk caused by the displacement (Δs) of the optical beam with respect to the focusing lens.

Fig. 11
Fig. 11

Plots for Δs as a function of wL for optical receivers with a 20- and a 30-dB dynamic range. The values of Δs and wL are normalized to wB (wB is assumed to equal 1 mm).

Fig. 12
Fig. 12

Plot of 1/p as a function of Δs for a value of BER = 10−12 and a receiver with a 20-dB dynamic range. The values of p and Δs are normalized to wB (wB = 1 mm), and the receiver parameters for the calculation are as described in the text.

Fig. 13
Fig. 13

Plots of the beam radius wB as a function of the propagation distance z for a wavelength of λ = 670 nm and a radius range of wB 0 = 0.2–0.6 mm, with an increment of 0.1 mm. wB 0 is the beam radius at the collimating lens.

Tables (3)

Tables Icon

Table 1 Expressions of the Optical-Link Efficiency for Signal Transmission

Tables Icon

Table 2 Optimized Optical-Link Efficiencies for the System Shown in Fig. 3

Tables Icon

Table 3 Design Examples for Optical Bus Systems with Maximum Interconnect Distances of 10 and 45 cm

Equations (15)

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η 0 = cos 2 2 ν ,
η 1 = η 2 = 1 2 sin 2 2 ν ,
ν = π n 1 T λ ( cos θ d ) 1 / 2 ,
η = 1 2 sin 2 2 ν ,
η + = 1 8 sin 2 2 2 ν ,
η 0 = 1 4 ( 1 + cos 2 2 ν ) 2 ,
η ave = 1 4 [ ( η AB + η AC + η AD ) + ( η BA + η BC + η BD ) + ( η CA + η CB + η CD ) + ( η DA + η DB + η DC ) ] = 1 2 ( η AB + 3 η AC + η CB + η CD ) ,
D = 10 log [ max ( η AB , η AC , η CB , η CD ) min ( η AB , η AC , η CB , η CD ) ] ,
M = ( η ave D ) ,
P ( d ) = 2 w B 2 0 2 π 0 w L exp [ 2 π w B 2 ( τ 2 2 τ d cos θ + d 2 ) ] × τ d τ d θ .
BER 1 2 π Q exp ( Q 2 2 ) ,
P ave = 1 2 ( P 0 + P 1 ) = P 1 2 ( 1 + r ) .
P ave = ( 1 + r ) ( 1 r ) Q R d i rx 2 1 / 2 ,
P 1 = 2 ( 1 r ) Q R d i rx 2 1 / 2 .
w B = w B 0 [ 1 + ( λ z w B 0 2 ) 2 ] 1 / 2 ,

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