Abstract

Ultimately low-loss 90° waveguide bend composed of clothoid and normal curves is proposed for dense optical interconnect photonic integrated circuits. By using clothoid curves at the input and output of 90° waveguide bend, straight and bent waveguides are smoothly connected without increasing the footprint. We found that there is an optimum ratio of clothoid curves in the bend and the bending loss can be significantly reduced compared with normal bend. 90% reduction of the bending loss for the bending radius of 4 μm is experimentally demonstrated with excellent agreement between theory and experiment. The performance is compared with the waveguide bend with offset, and the proposed bend is superior to the waveguide bend with offset in terms of fabrication tolerance.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2016 (1)

2013 (1)

2012 (3)

2011 (2)

2009 (1)

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

2006 (3)

2004 (1)

1996 (1)

S. Chulhun and J. C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol. 14(10), 2255–2259 (1996).
[Crossref]

Aalto, T.

M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
[Crossref] [PubMed]

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Akedo, J.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Baba, T.

Bogaerts, W.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

Chen, J. C.

S. Chulhun and J. C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol. 14(10), 2255–2259 (1996).
[Crossref]

Chen, T.

Cherchi, M.

Chulhun, S.

S. Chulhun and J. C. Chen, “Low transition losses in bent rib waveguides,” J. Lightwave Technol. 14(10), 2255–2259 (1996).
[Crossref]

Cunningham, J. E.

Dekker, J.

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Fujikata, J.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Furue, K.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Gomyo, A.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Greborio, L.

Hama, Y.

Harjanne, M.

M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
[Crossref] [PubMed]

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Heimala, P.

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Hibino, Y.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Hida, Y.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Ishi, T.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Ishikura, N.

Ishizaka, Y.

Itabashi, S.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Itoh, M.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Jiang, J.

Kakihara, K.

Kapulainen, M.

M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
[Crossref] [PubMed]

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Kawaguchi, Y.

Kim, S.

Kinoshita, M.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Kitoh, T.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Kominato, T.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Kono, N.

Koshiba, M.

Krishnamoorthy, A. V.

Lee, H.

Lee, J.-H.

Li, G.

Li, J.

Luo, Y.

McNab, S.

Mekis, A.

Mizuno, M.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Nakada, M.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Nishi, K.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Nordin, G. P.

Nose, K.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Ohashi, K.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Okamoto, D.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Olivero, M.

Orta, R.

Pellegrino, P.

Perrone, G.

Qian, Y.

Raj, K.

Regio, P.

Saitoh, K.

Selvaraja, S. K.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

Shimizu, T.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Shinkawa, M.

Shubin, I.

Sohma, S.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Solehmainen, K.

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Song, J.

Suzuki, K.

Suzuki, N.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Takahashi, H.

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

Thacker, H.

Torii, S.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Tsuchizawa, T.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Ueno, T.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Ushida, J.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Vahala, K. J.

Vlasov, Y.

Watanabe, T.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Yamada, K.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Yao, J.

Ylinen, S.

Yukawa, H.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Zheng, X.

Appl. Opt. (1)

IEEE Photonics J. (1)

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. A, Pure Appl. Opt. (1)

K. Solehmainen, T. Aalto, J. Dekker, M. Kapulainen, M. Harjanne, and P. Heimala, “Development of multi-step processing in silicon-on-insulator for optical waveguide applications,” J. Opt. A, Pure Appl. Opt. 8(7), S455–S460 (2006).
[Crossref]

Opt. Express (7)

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

Y. Qian, S. Kim, J. Song, G. P. Nordin, and J. Jiang, “Compact and low loss silicon-on-insulator rib waveguide 90° bend,” Opt. Express 14(13), 6020–6028 (2006).
[Crossref] [PubMed]

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14(23), 11128–11141 (2006).
[Crossref] [PubMed]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011).
[Crossref] [PubMed]

G. Li, J. Yao, H. Thacker, A. Mekis, X. Zheng, I. Shubin, Y. Luo, J.-H. Lee, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects,” Opt. Express 20(11), 12035–12039 (2012).
[Crossref] [PubMed]

T. Chen, H. Lee, J. Li, and K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20(20), 22819–22829 (2012).
[Crossref] [PubMed]

M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
[Crossref] [PubMed]

Proc. IEEE (1)

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, and J. Akedo, “On-Chip optical interconnect,” Proc. IEEE 97(7), 1186–1198 (2009).
[Crossref]

Other (3)

T. Kominato, Y. Hida, M. Itoh, H. Takahashi, S. Sohma, T. Kitoh, and Y. Hibino, “Extremely low-loss (0.3 dB/m) and long silica-based waveguides with large width and clothoid curve connection,” in Proceedings of European Conference on Optical Communication (ECOC), Sweden, Tu1.4.3 (2004).

X. Tu, M. Li, J. Jiang, D. Goodwill, P. Dumais, E. Bernier, H. Fu, and D. Geng, “Compact low-loss adiabatic bends in silicon shallow etched waveguides” in Proceedings of Group IV Photonics, China, ThA5 (2016).

S. Makino, M. Suga, T. Sato, T. Fujisawa, and K. Saitoh, “Ultimately low-loss and compact Si wire 90° waveguide bend composed of clothoid and normal curves for dense optical interconnect PICs” in Proceedings of Optical Fiber Communication Conference (OFC), USA, Th3E.2 (2017).
[Crossref]

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Figures (13)

Fig. 1
Fig. 1

Schematic of 90° waveguide bend composed of clothoid and normal curves.

Fig. 2
Fig. 2

(left) Top-view of bending waveguide and (right) the cross section of the Si-wire waveguide.

Fig. 3
Fig. 3

Bending loss as a function of the ratio of clothoid curve for Reff = 3, 4, and 5 µm.

Fig. 4
Fig. 4

Bending loss as a function of the ratio of clothoid curve for Reff = 2 μm.

Fig. 5
Fig. 5

Electric field distributions (log scale)of normal (left) and clothoid bend (right).

Fig. 6
Fig. 6

Micrographs of fabricated four bending waveguides.

Fig. 7
Fig. 7

Bending loss as a function of Nb.

Fig. 8
Fig. 8

Bending loss per 90° as a function of the ratio of clothoid curves.

Fig. 9
Fig. 9

Bending loss spectrum for Nb = 398.

Fig. 10
Fig. 10

Top-view of the offset bend.

Fig. 11
Fig. 11

Calculated transmission spectra of normal, clothoid, and offset bends (Reff = 4 µm).

Fig. 12
Fig. 12

Calculated bending loss of normal, clothoid, and offset bends as a function of Δw.

Fig. 13
Fig. 13

Calculated bending loss of the offset bend as a function of Δx.

Equations (5)

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x = A 0 L / A sin ( θ 2 2 ) d θ
z = A 0 L / A cos ( θ 2 2 ) d θ
R L = A 2
× ( [ μ r ] 1 × Ε ) k 0 2 [ ε r ] Ε = 0
[ P ] { E } = { E i n }

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