Abstract

We present an index profile design for remarkably low loss multimode optical crossed waveguide. In this paper, we theoretically calculate the light propagation loss in crossed waveguides with step-index (SI) and graded-index (GI) square cores utilizing a ray tracing simulation. In this simulation, we focus on the index exponent values for the GI profile, which allows low crossing loss even if the number of crossing is as large as 50 or even if the crossing angle is as low as 20°. It is revealed that an index exponent of 2.0 for the GI core strongly contributes to exhibit 35 times lower loss (0.072 dB after 50-perpendicular crosses) compared to the loss of the SI-core counterpart (2.58 dB after the same crossings). The GI cores with a smaller index exponent exhibit better loss in crossed waveguides with a wide range of crossing angles from 30° to 90°. Furthermore, we discuss the effect of the refractive index profile at the intersection on the optical loss of crossed waveguides.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Low-loss graded-index polymer crossed optical waveguide with high thermal resistance

Kohei Abe, Yutaro Oizumi, and Takaaki Ishigure
Opt. Express 26(4) 4512-4521 (2018)

References

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  1. http://www.top500.org/
  2. A. Benner, “Optical interconnect opportunities in supercomputers and high end computing,” in Optical Fiber Communication Conference and Exposition 2012, Paper OTu2B4.
  3. 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. Haung, 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]
  4. R. C. A. Pitwon, K. Wang, J. Graham-Jones, I. Papakonstantinou, H. Baghsiahi, B. J. Offrein, R. Dangel, D. Milward, and D. R. Selviah, “FirstLight: Pluggable optical interconnect technologies for polymeric electro-optical printed circuit boards in data centers,” J. Lightwave Technol. 30(21), 3316–3329 (2012).
    [Crossref]
  5. N. Bamiedakis, A. Hashim, R. V. Penty, and I. H. White, “A 40 Gb/s optical bus for optical backplane interconnections,” J. Lightwave Technol. 32(8), 1526–1537 (2014).
    [Crossref]
  6. 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,” J. Quantum Electron. 45(4), 415–424 (2009).
    [Crossref]
  7. F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).
  8. T. Ishigure and Y. Takeyoshi, “Polymer waveguide with 4-channel graded-index circular cores for parallel optical interconnects,” Opt. Express 15(9), 5843–5850 (2007).
    [Crossref] [PubMed]
  9. Y. Takeyoshi and T. Ishigure, “High-density 2×4 channel polymer optical waveguide with graded-index circular cores,” J. Lightwave Technol. 27(14), 2852–2861 (2009).
    [Crossref]
  10. K. Soma and T. Ishigure, “Fabrication of a graded-index circular-core polymer parallel optical waveguide using a microdispenser for a high-density optical printed circuit board,” IEEE J. Sel. Top. Quantum Electron. 19(2), 3600310 (2013).
    [Crossref]
  11. C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.
  12. B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
    [Crossref]
  13. T. Okoshi, Optical Fibers (Academic Press, 1982). Chapter 3.
  14. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1995), Part I.
  15. T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
    [Crossref]
  16. R. Olshansky and D. B. Keck, “Pulse broadening in graded-index optical fibers,” Appl. Opt. 15(2), 483–491 (1976).
    [Crossref] [PubMed]
  17. T. Ishigure and Y. Nitta, “Polymer optical waveguide with multiple graded-index cores for on-board interconnects fabricated using soft-lithography,” Opt. Express 18(13), 14191–14201 (2010).
    [Crossref] [PubMed]
  18. T. Mori, K. Moriya, K. Kitazoe, S. Takayama, S. Terada, M. Fujiwara, K. Takahama, K. Choki, and T. Ishigure, “Polymer optical waveguide having unique refractive index profiles for ultra high-density interconnection,” in Optical Fiber Communication Conference and Exposition 2012, Paper OTu1I6.
  19. T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
    [Crossref]
  20. P. Pepeljugoski, S. E. Golowich, A. J. Ritger, P. Kolesar, and A. Risteski, “Modeling and simulation of next-generation multimode fiber links,” J. Lightwave Technol. 21(5), 1242–1255 (2003).
    [Crossref]

2014 (1)

2013 (1)

K. Soma and T. Ishigure, “Fabrication of a graded-index circular-core polymer parallel optical waveguide using a microdispenser for a high-density optical printed circuit board,” IEEE J. Sel. Top. Quantum Electron. 19(2), 3600310 (2013).
[Crossref]

2012 (2)

2010 (3)

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

T. Ishigure and Y. Nitta, “Polymer optical waveguide with multiple graded-index cores for on-board interconnects fabricated using soft-lithography,” Opt. Express 18(13), 14191–14201 (2010).
[Crossref] [PubMed]

2009 (2)

Y. Takeyoshi and T. Ishigure, “High-density 2×4 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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

2007 (1)

2003 (1)

1976 (1)

Amb, C. M.

B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
[Crossref]

Baghsiahi, H.

Bajkowski, D.

Baks, C. W.

Bamiedakis, N.

N. Bamiedakis, A. Hashim, R. V. Penty, and I. H. White, “A 40 Gb/s optical bus for optical backplane interconnections,” J. Lightwave Technol. 32(8), 1526–1537 (2014).
[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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Berry, J.

Betschon, F.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Brown, C. T. A.

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

Budd, R. A.

Carver, C.

Chan, B.

Choki, K.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Craiovanc, D.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Dangel, R.

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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Dietrichb, K.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Doany, F. E.

Edwards, T. J.

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

Fujiwara, M.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Gmür, J. F. M.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Golowich, S. E.

Graham-Jones, J.

Halter, M.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Hashim, A.

Haung, J.

Hyer, M. G.

B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
[Crossref]

Ishigure, T.

K. Soma and T. Ishigure, “Fabrication of a graded-index circular-core polymer parallel optical waveguide using a microdispenser for a high-density optical printed circuit board,” IEEE J. Sel. Top. Quantum Electron. 19(2), 3600310 (2013).
[Crossref]

T. Ishigure and Y. Nitta, “Polymer optical waveguide with multiple graded-index cores for on-board interconnects fabricated using soft-lithography,” Opt. Express 18(13), 14191–14201 (2010).
[Crossref] [PubMed]

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

T. Ishigure and Y. Takeyoshi, “Polymer waveguide with 4-channel graded-index circular cores for parallel optical interconnects,” Opt. Express 15(9), 5843–5850 (2007).
[Crossref] [PubMed]

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

Jian, C.

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

John, R. S.

B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
[Crossref]

Kash, J. A.

Keck, D. B.

Knickerbocker, J. U.

Kolesar, P.

Kremmelb, J.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Kudo, T.

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

Lee, B. G.

Libsch, F.

Lin, H.

Michlerb, M.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Milward, D.

Mori, T.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

Moriya, K.

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

Nitta, Y.

Offrein, B. J.

Olshansky, R.

Owari, H.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Papakonstantinou, I.

Paredes, S.

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Penty, R. V.

N. Bamiedakis, A. Hashim, R. V. Penty, and I. H. White, “A 40 Gb/s optical bus for optical backplane interconnections,” J. Lightwave Technol. 32(8), 1526–1537 (2014).
[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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

Pepeljugoski, P.

Pitwon, R. C. A.

Risteski, A.

Ritger, A. J.

Sakamoto, M.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Schow, C. L.

Selviah, D. R.

Shirato, Y.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Shitanda, K.

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

Soma, K.

K. Soma and T. Ishigure, “Fabrication of a graded-index circular-core polymer parallel optical waveguide using a microdispenser for a high-density optical printed circuit board,” IEEE J. Sel. Top. Quantum Electron. 19(2), 3600310 (2013).
[Crossref]

Swatowski, B. W.

B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
[Crossref]

Takahama, K.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Takayama, S.

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

Takeyoshi, Y.

Terada, S.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Tsang, C. K.

Wang, K.

Watanabe, K.

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

Weidner, W. K.

B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
[Crossref]

White, I. H.

N. Bamiedakis, A. Hashim, R. V. Penty, and I. H. White, “A 40 Gb/s optical bus for optical backplane interconnections,” J. Lightwave Technol. 32(8), 1526–1537 (2014).
[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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

K. Soma and T. Ishigure, “Fabrication of a graded-index circular-core polymer parallel optical waveguide using a microdispenser for a high-density optical printed circuit board,” IEEE J. Sel. Top. Quantum Electron. 19(2), 3600310 (2013).
[Crossref]

J. Lightwave Technol. (5)

J. Quantum Electron. (1)

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,” J. Quantum Electron. 45(4), 415–424 (2009).
[Crossref]

Opt. Express (2)

Proc. SPIE (2)

T. Mori, K. Takahama, M. Fujiwara, K. Watanabe, H. Owari, Y. Shirato, S. Terada, M. Sakamoto, and K. Choki, “Optical and electrical hybrid flexible printed circuit boards with unique photo-defined polymer waveguide layers,” Proc. SPIE 7607, 76070S (2010).
[Crossref]

F. Betschon, M. Michlerb, D. Craiovanc, M. Halter, K. Dietrichb, J. Kremmelb, J. F. M. Gmür, and S. Paredes, “Mass production of planar polymer waveguides and their applications,” Proc. SPIE 7607, 76070M (2010).

Other (8)

http://www.top500.org/

A. Benner, “Optical interconnect opportunities in supercomputers and high end computing,” in Optical Fiber Communication Conference and Exposition 2012, Paper OTu2B4.

C. Jian, N. Bamiedakis, T. J. Edwards, C. T. A. Brown, R. V. Penty, and I. H. White, “Dispersion studies on multimode polymer spiral waveguides for board-level optical interconnects,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2015), pp. 26–27.

B. W. Swatowski, C. M. Amb, M. G. Hyer, R. S. John, and W. K. Weidner, “Graded index silicone waveguides for high performance computing,” in Proceedings of IEEE Optical Interconnects Conference (IEEE, 2014), pp. 133–134.
[Crossref]

T. Okoshi, Optical Fibers (Academic Press, 1982). Chapter 3.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1995), Part I.

T. Mori, K. Moriya, K. Kitazoe, S. Takayama, S. Terada, M. Fujiwara, K. Takahama, K. Choki, and T. Ishigure, “Polymer optical waveguide having unique refractive index profiles for ultra high-density interconnection,” in Optical Fiber Communication Conference and Exposition 2012, Paper OTu1I6.

T. Ishigure, K. Shitanda, T. Kudo, S. Takayama, T. Mori, K. Moriya, and K. Choki, “Low-loss design and fabrication of multimode polymer optical waveguide circuit with crossings for high-density optical PCB,” inProceedings of Electronics Components and Technology Conference, 297–304 (2013).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Model structure of crossed waveguides for simulation.
Fig. 2
Fig. 2 Calculated optical loss from SI- and GI-core crossed waveguides.
Fig. 3
Fig. 3 Difference of ray trajectory between SI- and GI-core crossed waveguides.
Fig. 4
Fig. 4 Crossing loss dependence on (a) the refractive index (nint) at the intersection and (b) core size.
Fig. 5
Fig. 5 Accumulated crossing loss dependence on the index exponent (a) with respect to the number of crossing (b) crossing loss comparison after 20 and 50 crossings.
Fig. 6
Fig. 6 Variation of refractive index profiles expressed by the power-law form with different index exponent.
Fig. 7
Fig. 7 Accumulated crossing loss of SI- and GI-core crossed waveguides after 50 crossings with respect to the launch beam spot size.
Fig. 8
Fig. 8 Influence of offset launch on accumulated crossing loss in the SI- (p = q = 40) and GI-core (p = q = 3) crossed waveguides.
Fig. 9
Fig. 9 Classification of ray-leakage point in GI- and SI-core crossed waveguides.
Fig. 10
Fig. 10 Crossing angle dependence of SI- and GI-core crossed waveguides.

Equations (5)

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d ds [ n( r ) dr ds ]={ n( r ) }
n( x,y )= n co [ 12Δ{ f( x )+g( y ) } ] 1 2
f( x )= | x a x | p , g( y )= | y a y | q , Δ= n co 2 n cl 2 2 n co 2
f( x )+g( y )1,
n( x,y )= n cl

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