Abstract

We theoretically analyze the origin of inter-channel crosstalk in densely aligned multimode parallel optical waveguides for on-board interconnects using the Beam Propagation Method. In this paper, we demonstrate that the inter-channel crosstalk due to mode coupling is very low in graded-index (GI) circular-core waveguides because the propagation constants of the propagating modes are discrete. Additionally, it is also found that the waveguides with GI-type circular cores is sensitive to the optical confinement in the cladding: low-power cladding modes largely decrease the mode conversion.

© 2014 Optical Society of America

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  1. F. E. Doany, C. L. Schow, B. G. Lee, R. A. Budd, C. W. Baks, C. K. Tsang, J. U. Knickerbocker, R. Dangel, B. Chan, H. Lin, C. Carver, J. Huang, J. Berry, D. Bajkowski, F. Libsch, and J. A. Kash, “Terabit/s-class optical PCB links incorporating 360-Gb/s bidirectional 850 nm parallel optical transceivers,” J. Lightwave Technol. 30(4), 560–571 (2012).
    [Crossref]
  2. R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
    [Crossref]
  3. Y. Takeyoshi and T. Ishigure, “High-density 2 x 4 channel polymer optical waveguide with graded-index circular cores,” J. Lightwave Technol. 27(14), 2852–2861 (2009).
    [Crossref]
  4. H.-H. Hsu, Y. Hirobe, and T. Ishigure, “Fabrication and inter-channel crosstalk analysis of polymer optical waveguides with W-shaped index profile for high-density optical interconnections,” Opt. Express 19(15), 14018–14030 (2011).
    [Crossref] [PubMed]
  5. N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
    [Crossref]
  6. M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
    [Crossref]
  7. S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method,” IEEE J. Quantum Electron. 30(9), 2098–2105 (1994).
    [Crossref]
  8. T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
    [Crossref]
  9. T. Kudo and T. Ishigure, “Analysis of inter-channel crosstalk in multi-mode parallel optical waveguide using beam propagation method,” in Proc. of IEEE Components, Packaging and Manufacturing Technology Symposium, Japan (2012).
    [Crossref]
  10. T. Ishigure, Y. Koike, and J. W. Fleming, “Optimum index profile of the perfluorinated polymer-based GI polymer optical fiber and its dispersion properties,” J. Lightwave Technol. 18(2), 178–184 (2000).
  11. M. J. Adams, D. N. Payne, and F. M. E. Sladen, “Length-dependent effects due to leaky modes on multimode graded-index optical fibres,” Opt. Commun. 17(2), 204–209 (1976).
    [Crossref]

2012 (1)

2011 (1)

2009 (3)

Y. Takeyoshi and T. Ishigure, “High-density 2 x 4 channel polymer optical waveguide with graded-index circular cores,” J. Lightwave Technol. 27(14), 2852–2861 (2009).
[Crossref]

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

2008 (1)

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

2000 (1)

1997 (1)

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

1994 (1)

S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method,” IEEE J. Quantum Electron. 30(9), 2098–2105 (1994).
[Crossref]

1976 (1)

M. J. Adams, D. N. Payne, and F. M. E. Sladen, “Length-dependent effects due to leaky modes on multimode graded-index optical fibres,” Opt. Commun. 17(2), 204–209 (1976).
[Crossref]

Adams, M. J.

M. J. Adams, D. N. Payne, and F. M. E. Sladen, “Length-dependent effects due to leaky modes on multimode graded-index optical fibres,” Opt. Commun. 17(2), 204–209 (1976).
[Crossref]

Bajkowski, D.

Baks, C. W.

Bamiedakis, N.

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Beals, J.

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Berger, C.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Berry, J.

Beyeler, R.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Budd, R. A.

Carver, C.

Chan, B.

Chen, J. C.

S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method,” IEEE J. Quantum Electron. 30(9), 2098–2105 (1994).
[Crossref]

Clapp, T. V.

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Dangel, R.

F. E. Doany, C. L. Schow, B. G. Lee, R. A. Budd, C. W. Baks, C. K. Tsang, J. U. Knickerbocker, R. Dangel, B. Chan, H. Lin, C. Carver, J. Huang, J. Berry, D. Bajkowski, F. Libsch, and J. A. Kash, “Terabit/s-class optical PCB links incorporating 360-Gb/s bidirectional 850 nm parallel optical transceivers,” J. Lightwave Technol. 30(4), 560–571 (2012).
[Crossref]

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

DeGroot, J. V.

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Dellmann, L.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Doany, F. E.

Fleming, J. W.

Gmur, M.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Hamelin, R.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Hirobe, Y.

Horst, F.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Hsu, H.-H.

Huang, J.

Ishigure, T.

Jungling, S.

S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method,” IEEE J. Quantum Electron. 30(9), 2098–2105 (1994).
[Crossref]

Kash, J. A.

Knickerbocker, J. U.

Koike, Y.

T. Ishigure, Y. Koike, and J. W. Fleming, “Optimum index profile of the perfluorinated polymer-based GI polymer optical fiber and its dispersion properties,” J. Lightwave Technol. 18(2), 178–184 (2000).

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

Kokubun, Y.

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

Koshiba, M.

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

Lamprecht, T.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Lee, B. G.

Libsch, F.

Lin, H.

Morf, T.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Nihei, E.

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

Nyu, T.

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

Offrein, B. J.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Oggioni, S.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Payne, D. N.

M. J. Adams, D. N. Payne, and F. M. E. Sladen, “Length-dependent effects due to leaky modes on multimode graded-index optical fibres,” Opt. Commun. 17(2), 204–209 (1976).
[Crossref]

Penty, R. V.

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Saitoh, K.

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

Satoh, M.

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

Schow, C. L.

Sladen, F. M. E.

M. J. Adams, D. N. Payne, and F. M. E. Sladen, “Length-dependent effects due to leaky modes on multimode graded-index optical fibres,” Opt. Commun. 17(2), 204–209 (1976).
[Crossref]

Spreafico, M.

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

Takanashi, O.

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

Takeyoshi, Y.

Tsang, C. K.

White, I. H.

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Yamazaki, S.

T. Ishigure, M. Satoh, O. Takanashi, E. Nihei, T. Nyu, S. Yamazaki, and Y. Koike, “Formation of the refractive index profile in the graded index polymer optical fiber for gigabit data transmission,” J. Lightwave Technol. 15(11), 2095–2100 (1997).
[Crossref]

IEEE J. Quantum Electron. (2)

N. Bamiedakis, J. Beals, R. V. Penty, I. H. White, J. V. DeGroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method,” IEEE J. Quantum Electron. 30(9), 2098–2105 (1994).
[Crossref]

IEEE Trans. Adv. Packag. (1)

R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmur, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for datacom applications,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008).
[Crossref]

IEICE Electron. Express (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

J. Lightwave Technol. (4)

Opt. Commun. (1)

M. J. Adams, D. N. Payne, and F. M. E. Sladen, “Length-dependent effects due to leaky modes on multimode graded-index optical fibres,” Opt. Commun. 17(2), 204–209 (1976).
[Crossref]

Opt. Express (1)

Other (1)

T. Kudo and T. Ishigure, “Analysis of inter-channel crosstalk in multi-mode parallel optical waveguide using beam propagation method,” in Proc. of IEEE Components, Packaging and Manufacturing Technology Symposium, Japan (2012).
[Crossref]

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Figures (17)

Fig. 1
Fig. 1 The distribution of normalized propagation constants [9] (2a = 35.0 μm, n1 = 1.50, n2 = 1.49, g = 2.0).
Fig. 2
Fig. 2 Index-profile of GI-type square core (n1 = 1.5, n2 = 1.49, g = 2) (a) 2D-image; (b) 1D-description.
Fig. 3
Fig. 3 The concept of mode coupling between multimode channels.(a) The continuous distribution; (b) The discrete distribution.
Fig. 4
Fig. 4 Simulation model.
Fig. 5
Fig. 5 Relationships between δn and XT (left: GI-circular, center: GI-square, right: SI-square).
Fig. 6
Fig. 6 Relationships between δd and XT (left: GI-circular, center: GI-square, right: SI-square).
Fig. 7
Fig. 7 Relationships between δg and XT (left: GI-circular, right: GI-square).
Fig. 8
Fig. 8 Near-field pattern after a 10-cm propagation when Ch. 1 (right hand side) is excited. (a) GI-circular; (b) GI-square; (c) SI-square (two cores have the same core-index); (d) GI-circular; (e) GI-square; (f) SI-square (two cores have different core-indexes; δn is set to be 5.0 x 10−4).
Fig. 9
Fig. 9 Observed NFP from a GI-core polymer waveguide [3].
Fig. 10
Fig. 10 NFP after a 10-cm waveguide propagation when the light is coupled to the cladding (A smooth boundary between the cladding and outer medium is assumed.) (a) GI-circular; b) GI-square; c) SI-square), X: injected point of Gaussian beam.
Fig. 11
Fig. 11 NFP after a 10-cm waveguide propagation when the light is coupled to the cladding (A rough boundary between cladding-outer medium is assumed) (a) GI-circular; b) GI-square; c) SI-square), X: injected point of Gaussian beam.
Fig. 12
Fig. 12 Simulation model.
Fig. 13
Fig. 13 Relationships between the cladding margin and XT (left: GI-circular, center: GI-square, right: SI-square).
Fig. 14
Fig. 14 Relationships between δn and XT (left: GI-circular, center: GI-square, right: SI-square).
Fig. 15
Fig. 15 Near-field pattern after a 10-cm propagation (a) GI-circular; (b) GI-square; (c) SI-square (two cores have the same core-index) (d) SI-circular; (e) GI-square; (f) SI-square (two cores have different core-index; δn is set to be −5.0 x 10−4).
Fig. 16
Fig. 16 Near-field pattern after a 10-cm propagation (GI-circular; two cores have different core-index).
Fig. 17
Fig. 17 Near-field pattern after a 10-cm propagation (62.5-μm pitch) (a) GI-circular; (b) GI-square; (c) SI-square (two cores have the same core-index) (d) SI-circular; (e) GI-square; (f) SI-square (two cores have different core-indexes; δn is set to be 5.0 x 10−4).

Tables (6)

Tables Icon

Table 1 Structural parameters

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Table 2 Structural parameters

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Table 3 Ratio of averaged Poynting vector in core to cladding

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Table 4 Structural parameters

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Table 5 Inter-channel crosstalk when the core is excited using 35-μm MMFs compared to the crosstalk when a Gaussian beam is injected

Tables Icon

Table 6 Inter-channel crosstalk when core-pitch is set to be 62.5 μm

Equations (11)

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

η= 1 1+ ( β 2 β 1 2κ ) 2
E= m ϕ m exp[i β m z]
E= m ϕ m exp[ β m τ]
n(x,y)={ n 1 [ 12Δ ( ( x 2 + y 2 ) 1 2 a ) g ] 1 2 0 ( x 2 + y 2 ) 1 2 a n 1 [12Δ] 1 2 a ( x 2 + y 2 ) 1 2
n(x,y)={ n 1 [ 12Δ( | x a | g + | y a | g | xy a 2 | g ) ] 1 2 0( | x a | g + | y a | g | xy a 2 | g )1 n 1 [12Δ] 1 2 otherwise
Δ= n 1 2 n 2 2 2 n 1 2
b m = β m minβ maxβminβ
R(u)= σ 2 exp[|u|/D]
R(u)= h(z)h(zu)dz
XT=10 log 10 ( P Ch.2 / P Ch.1 )
C= < p core > < p cladding >

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