Abstract

Topology optimization has been used to design a 60° bend in a single-mode planar photonic crystal waveguide. The design has been realized in a silicon-on-insulator material and we demonstrate a record-breaking 200nm transmission bandwidth with an average bend loss of 0.43±0.27 dB for the TE polarization. The experimental results agree well with 3D finite-difference-time-domain simulations.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett.

J. S. Jensen and O. Sigmund, �??Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,�?? Appl. Phys. Lett. 84, 2022-2024 (2004).
[CrossRef]

Appl. Phys.Lett.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, M. Agio, �??Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm,�?? Appl. Phys.Lett. 80, 547-549 (2002).
[CrossRef]

A. Chutinan, M. Okano, S. Noda, �??Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,�?? Appl. Phys.Lett. 80, 1698-1700 (2002).
[CrossRef]

Electron. Lett.

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, S. Beckx, �??Bandwidth tuning of photonic crystal waveguide bends,�?? Electron. Lett. 40, 1263-1264 (2004).
[CrossRef]

IEICE Trans. Electron.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, K. Asakawa, �??Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,�?? IEICE Trans. Electron. E87-C, 316-327 (2004).

Int. J. Numer. Meth. Engng.

K. Svanberg, �??The method of moving asymptotes: a new method for structural optimization,�?? Int. J. Numer. Meth. Engng. 24, 359-373 (1987).
[CrossRef]

J. Lightwave Technol.

Nature

T. F. Krauss, R. M. De La Rue, and S. Brand, �??Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,�?? Nature 383, 699-702 (1996).
[CrossRef]

Opt. Express

J. Smajic, C. Hafner, D. Erni, �??Design and optimization of an achromatic photonic crystal bend,�?? Opt. Express 11, 1378-1384 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1378.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1378.</a>
[CrossRef] [PubMed]

P.I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, Y. X. Zhuang, M. Kristensen, and H. M. H. Chong, �??Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light.�?? Opt. Express 11, 1757-1762 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757.</a>
[CrossRef] [PubMed]

A. Lavrinenko, P.I. Borel, L.H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen and T. Niemi, �??Comprehensive FDTD Modelling of Photonic Crystal Waveguide Components,�?? Opt. Express 12, 234-248 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234.</a>
[CrossRef] [PubMed]

P.I. Borel, A. Harpøth, L.H. Frandsen, M. Kristensen, P. Shi, J.S. Jensen and O. Sigmund, �??Topology Optimization and fabrication of photonic crystal structures,�?? Opt. Express 12, 1996�??2001 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.</a>
[CrossRef] [PubMed]

R. L. Espinola, R. U. Ahmad, F. Pizzuto, M. J. Steel, R. M. Osgood, Jr., �??A study of high-index contrast 90° waveguide bend structures,�?? Opt. Express 8, 517-528 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517.</a>
[CrossRef] [PubMed]

Opt. Lett.

Phil. Trans. R. Soc. Lond. A

O. Sigmund and J. S. Jensen, �??Systematic design of phononic band gap materials and structures by topology optimization,�?? Phil. Trans. R. Soc. Lond. A 361, 1001-1019 (2003).
[CrossRef]

Photonics and Nanostructures

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, U. Gösele, �??Silicon-based two-dimensional photonic crystal waveguides,�?? Photonics and Nanostructures �?? Fundamentals and Applications 1, 1-13 (2003).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Other

M. P. Bendsøe and O. Sigmund, Topology optimization �?? Theory, Methods and Applications (Springer-Verlag, 2003).

J. S. Jensen and O. Sigmund, �??Topology optimization of photonic crystal structures: A high bandwidth low loss T-junction waveguide,�?? J. Opt. Soc. Am. B, accepted (2004).

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Figures (5)

Fig. 1.
Fig. 1.

Schematics of photonic crystal waveguides containing two consecutive 60° bends. Left: Generic bend configuration. The red areas illustrate the chosen design domains in the topology optimization procedure. Right: Topology-optimized bends. The green areas highlight the optimized structures showing that a non-trivial smoothening has been applied to the bend.

Fig. 2.
Fig. 2.

Scanning electron micrographs of fabricated photonic crystal waveguides containing two consecutive 60° bends. The pitch of the triangular lattice is Λ≈400nm with hole diameter D≈275nm. Left: Waveguide with generic. Right: Waveguide with topology-optimized bends. The number, shape and size of the holes at each bend are designed using topology optimization. The contrast and brightness of the images have been changed for clarity.

Fig. 3.
Fig. 3.

Steady-state magnetic field distribution for the fundamental PBG mode simulated using 2D FDTD. The mode is incident from the bottom-left part of the waveguide. Left: Mode profile through the generic bends. Right: Mode profile through the topology-optimized bends.

Fig. 4.
Fig. 4.

Measured loss per bend for the un-optimized 60° bends (red) and the topology-optimized 60° bends (green). Both spectra have been normalized to the transmission through straight PhCWs of the same length to eliminate the coupling and the propagation loss in straight waveguides. Dotted line marks a bend loss of 1dB.

Fig. 5.
Fig. 5.

Experimental bend loss (green) compared to 3D FDTD calculated bend loss (blue). The 3D FDTD curve has been shifted 1.2% in absolute wavelength.

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