Abstract

We demonstrate theoretically and experimentally how highly multimodal high index contrast waveguides with micron-scale cores can be bent, on an ultra-broad band of operation, with bending radii below 10 µm and losses for the fundamental mode below 0.02 dB/90°. The bends have been designed based on the Euler spiral and fabricated on 4 µm thick SOI. The proposed approach enabled also the realization of 180° bends with 1.27 µm effective radii and 0.09 dB loss, which are the smallest low-loss bends ever reported for an optical waveguide. These results pave the way for unprecedented integration density in most semiconductor platforms.

© 2013 OSA

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2012

2011

W. Yuan and D. C. Hall, “A General Scaling Rule for Matched Bend Waveguides,” J. Lightwave Technol.29(24), 3786–3796 (2011).
[CrossRef]

W. Yuan, C. S. Seibert, and D. C. Hall, “Single-Facet Teardrop Laser With Matched-Bends Design,” IEEE J. Sel. Top. Quantum Electron.17(6), 1662–1669 (2011).
[CrossRef]

2010

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

P. Dong, W. Qian, H. Liang, R. Shafiiha, N.-N. Feng, D. Feng, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express18(10), 9852–9858 (2010).
[CrossRef] [PubMed]

2008

R. N. Sheehan, S. Horne, and F. H. Peters, “The design of low-loss curved waveguides,” Opt. Quantum Electron.40(14-15), 1211–1218 (2008).
[CrossRef]

2007

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett.32(19), 2801–2803 (2007).
[CrossRef] [PubMed]

Z. Hu and Y. Y. Lu, “Computing Optimal Waveguide Bends With Constant Width,” J. Lightwave Technol.25(10), 3161–3167 (2007).
[CrossRef]

2006

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express14(9), 3853–3863 (2006).
[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]

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-Loss Converters Between Optical Silicon Waveguides of Different Sizes and Types,” IEEE Photon. Technol. Lett.18(5), 709–711 (2006).
[CrossRef]

2005

M. Kohtoku, T. Kominato, Y. Nasu, and T. Shibata, “New Waveguide Fabrication Techniques for Next-generation PLCs,” NTT Tech. Rev.3, 37–41 (2005).

D. Lenz, D. Erni, and W. Bächtold, “Quasi-analytic formalism for mode characteristics in highly overmoded rectangular dielectric waveguide bends,” J. Opt. Soc. Am. A22(9), 1968–1975 (2005).
[CrossRef] [PubMed]

2004

2003

2002

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, “Integrated waveguide turning mirror in silicon-on-insulator,” IEEE Photon. Technol. Lett.14(1), 68–70 (2002).
[CrossRef]

2001

1998

1992

D. S. Meek and D. J. Walton, “Clothoid spline transition spirals,” Math. Comput.59(199), 117–133 (1992).
[CrossRef]

1991

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib wave-guides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron.27(8), 1971–1974 (1991).
[CrossRef]

1983

1969

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J.48, 2103–2132 (1969).

1957

H. G. Unger, “Normal Mode Bends for Circular Electric Waves,” Bell Syst. Tech. J.36, 1292–1307 (1957).

Aalto, T.

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-Loss Converters Between Optical Silicon Waveguides of Different Sizes and Types,” IEEE Photon. Technol. Lett.18(5), 709–711 (2006).
[CrossRef]

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]

M. Harjanne and T. Aalto, “Design of tight bends in silicon-on-insulator ridge waveguides,” Phys. Scr. T114, 209–212 (2004).
[CrossRef]

Asghari, M.

Bächtold, W.

Baehr-Jones, T.

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

Baets, R.

Barwicz, T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Ben Bakir, B.

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

Bogaerts, W.

Borreman, A.

Carniel, F.

Chen, T.

Costa, R.

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]

Diemeer, M. B. J.

Dong, P.

Driessen, A.

Dulkeith, E.

Dumon, P.

Erni, D.

Fedeli, J. M.

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

Feng, D.

Feng, N.-N.

Freude, W.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Green, W. M. J.

Hall, D. C.

W. Yuan and D. C. Hall, “A General Scaling Rule for Matched Bend Waveguides,” J. Lightwave Technol.29(24), 3786–3796 (2011).
[CrossRef]

W. Yuan, C. S. Seibert, and D. C. Hall, “Single-Facet Teardrop Laser With Matched-Bends Design,” IEEE J. Sel. Top. Quantum Electron.17(6), 1662–1669 (2011).
[CrossRef]

Harjanne, M.

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]

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-Loss Converters Between Optical Silicon Waveguides of Different Sizes and Types,” IEEE Photon. Technol. Lett.18(5), 709–711 (2006).
[CrossRef]

M. Harjanne and T. Aalto, “Design of tight bends in silicon-on-insulator ridge waveguides,” Phys. Scr. T114, 209–212 (2004).
[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]

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-Loss Converters Between Optical Silicon Waveguides of Different Sizes and Types,” IEEE Photon. Technol. Lett.18(5), 709–711 (2006).
[CrossRef]

Hochberg, M.

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

Horne, S.

R. N. Sheehan, S. Horne, and F. H. Peters, “The design of low-loss curved waveguides,” Opt. Quantum Electron.40(14-15), 1211–1218 (2008).
[CrossRef]

Hu, Z.

Ippen, E. P.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Jacome, L.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Kapulainen, M.

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-Loss Converters Between Optical Silicon Waveguides of Different Sizes and Types,” IEEE Photon. Technol. Lett.18(5), 709–711 (2006).
[CrossRef]

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]

Kärtner, F. X.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Kohtoku, M.

M. Kohtoku, T. Kominato, Y. Nasu, and T. Shibata, “New Waveguide Fabrication Techniques for Next-generation PLCs,” NTT Tech. Rev.3, 37–41 (2005).

Kok, A. A. M.

Kominato, T.

M. Kohtoku, T. Kominato, Y. Nasu, and T. Shibata, “New Waveguide Fabrication Techniques for Next-generation PLCs,” NTT Tech. Rev.3, 37–41 (2005).

Koos, C.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Krishnamoorthy, A. V.

Lagasse, P. E.

Lee, H.

Lee, J.-H.

Lenz, D.

Leuthold, J.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Li, G.

Li, J.

Li, T.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, “Integrated waveguide turning mirror in silicon-on-insulator,” IEEE Photon. Technol. Lett.14(1), 68–70 (2002).
[CrossRef]

Liang, H.

Lu, Y. Y.

Luo, Y.

Lyan, P.

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

Marcatili, E. A. J.

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J.48, 2103–2132 (1969).

Martinelli, M.

McNab, S.

Meek, D. S.

D. S. Meek and D. J. Walton, “Clothoid spline transition spirals,” Math. Comput.59(199), 117–133 (1992).
[CrossRef]

Mekis, A.

Melloni, A.

Monguzzi, P.

Musa, S.

Nasu, Y.

M. Kohtoku, T. Kominato, Y. Nasu, and T. Shibata, “New Waveguide Fabrication Techniques for Next-generation PLCs,” NTT Tech. Rev.3, 37–41 (2005).

Orobtchouk, R.

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

Petermann, K.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib wave-guides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron.27(8), 1971–1974 (1991).
[CrossRef]

Peters, F. H.

R. N. Sheehan, S. Horne, and F. H. Peters, “The design of low-loss curved waveguides,” Opt. Quantum Electron.40(14-15), 1211–1218 (2008).
[CrossRef]

Pogossian, S. P.

Popovic, M. A.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Porzier, C.

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

Poulton, C. G.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Qian, W.

Raj, K.

Rakich, P. T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Roman, A.

B. Ben Bakir, A. Vazquez de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J. M. Fedeli, “Low-Loss (<1 dB) and Polarization-Insensitive Edge Fiber Couplers Fabricated on 200-mm Silicon-on-Insulator Wafers,” IEEE Photon. Technol. Lett.22(11), 739–741 (2010).

Schares, L.

Schmidtchen, J.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib wave-guides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron.27(8), 1971–1974 (1991).
[CrossRef]

Seibert, C. S.

W. Yuan, C. S. Seibert, and D. C. Hall, “Single-Facet Teardrop Laser With Matched-Bends Design,” IEEE J. Sel. Top. Quantum Electron.17(6), 1662–1669 (2011).
[CrossRef]

Shafiiha, R.

Sheehan, R. N.

R. N. Sheehan, S. Horne, and F. H. Peters, “The design of low-loss curved waveguides,” Opt. Quantum Electron.40(14-15), 1211–1218 (2008).
[CrossRef]

Shibata, T.

M. Kohtoku, T. Kominato, Y. Nasu, and T. Shibata, “New Waveguide Fabrication Techniques for Next-generation PLCs,” NTT Tech. Rev.3, 37–41 (2005).

Shubin, I.

Smith, H. I.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Socci, L.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics1(1), 57–60 (2007).
[CrossRef]

Solehmainen, K.

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-Loss Converters Between Optical Silicon Waveguides of Different Sizes and Types,” IEEE Photon. Technol. Lett.18(5), 709–711 (2006).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Micron-scale silicon photonics platform. (a) Single mode rib waveguides can be tightly bent by TIR mirrors with 0.3 dB/90° loss; they can be also be turned into strip waveguides by almost lossless converters; (b) groove bends have been previously explored to reduce the bend size without affecting the losses; (c) in this work we propose to use suitably designed bends of multimode strip waveguides to dramatically reduce bend size and losses.

Fig. 2
Fig. 2

Simulated coupling to higher order modes at the output of multimode 90° bends as a function of the radius (TE polarization). (a) Arc in a 2 µm wide and 4 µm thick silicon strip waveguide. (b) Euler L-bend with the same waveguide structure.

Fig. 3
Fig. 3

Euler bend layouts. (a) Linear change of curvature as a function of path length s in a mirror-symmetric Euler-bend. (b) Example application to a 90° bend (L-bend) with normalized minimum bending radius Rmin = 1. The corresponding effective bending radius Reff is highlighted. The path length is π; (c) Same as b. but for a 180° bend (U-bend). The path length is 2π; (d) 2D Finite Element Frequency Domain simulation of light propagation in a U-bend with 900 nm waveguide width and 960 nm minimum bending radius (electric field, TE polarization). The field pattern clearly shows how, in a matched-bend, HOMs are indeed excited, but finally coupled back to the fundamental mode.

Fig. 4
Fig. 4

Simulated excitation of TE modes at the output of different bends as a function of wavelength. All bends are made in 2 µm wide and 4 µm thick silicon strip waveguides. (a) Matched 90° arc with 33.5 µm bending radius. The rectangle highlights the narrow operation bandwidth; (b) Adiabatic arc with 400 µm bending radius; (c) Euler L-bend with an effective radius of 17.2 µm. Its wide operation bandwidth is highlighted; (d) Matched Euler L-bend with an effective radius of 39.8 µm; (e) Adiabatic Euler L-bend with an effective radius of 74.8 µm.

Fig. 5
Fig. 5

Experimental results. (a) Measured scaling of losses with the number of bends for different U-bends (at 1.55 µm wavelength); (b) Spectral responses of cascaded Euler L-bends and 44 TIR mirrors (TE polarization); (c) SEM picture of some waveguide structures patterned into a 4 µm thick SOI layer with different number of bends and different bending radii; (d) SEM picture of a cascade of four U-bends in a 2 µm wide waveguide with 7.5 µm effective bending radius

Equations (2)

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1 R = dθ ds s θ ,
s=2Rθ.

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