Abstract

Topology optimization is used to design a planar photonic crystal waveguide component resulting in significantly enhanced functionality. Exceptional transmission through a photonic crystal waveguide Z-bend is obtained using this inverse design strategy. The design has been realized in a silicon-on-insulator based photonic crystal waveguide. A large low loss bandwidth of more than 200 nm for the TE polarization is experimentally confirmed.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett. (2)

M. Tokushima, H. Kosaka, A. Tomita and H.Yamada, �??Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,�?? Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

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]

Comput. Meth. Appl. Mech. Eng. (1)

M. P. Bendsøe and N. Kikuchi, �??Generating optimal topologies in structural design using a homogenization method,�?? Comput. Meth. Appl. Mech. Eng. 71, 197-224 (1988).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. Taillaert, H. Chong, P.I. Borel, L.H. Frandsen, R.M. De La Rue, and R. Baets, �??A Compact Two-dimensional Grating Coupler used as a Polarization Splitter,�?? IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).
[CrossRef]

Int. J. Numer. Meth. Engng. (1)

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

J. Opt. Soc. Am. B (1)

Microwave Opt. Technol. Lett. (1)

T. Uusitupa, K. Kärkkäinen and K. Nikoskinen, �??Studying 120° PBG waveguide bend using FDTD,�?? Microwave Opt. Technol. Lett. 39, 326-333 (2003).
[CrossRef]

Nature (1)

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 (3)

Opt. Lett. (2)

M. Thorhauge, L. H. Frandsen and P. I. Borel, �??Efficient Photonic Crystal Directional Couplers,�?? Opt. Lett. 28, 1525-1527 (2003).
[CrossRef] [PubMed]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, �??Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,�?? Opt. Lett. (to be published).

Phil. Trans. R. Soc. Lond. A (1)

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]

Phys. Rev. Lett. (2)

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]

Proc. SPIE (1)

T. P. Felici and D. F. G. Gallagher, �??Improved waveguide structures derived from new rapid optimization techniques,�?? Proc. SPIE 4986, 375-385 (2003).
[CrossRef]

Other (2)

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

It should be emphasized that the method can readily be implemented in a 3D finite element model where the computational requirements naturally will be significantly higher.

Supplementary Material (2)

» Media 1: MOV (150 KB)     
» Media 2: MOV (482 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Top: Standard and two modified Z-bend waveguides. Bottom: Transmission through the bends calculated using a 2D frequency domain finite element model.

Fig. 2.
Fig. 2.

Left: Schematic illustration of the topology optimization procedure. The yellow area sketches the design domain of one bend. Middle: (149 kB) Movie of how the material is redistributed in the design domain in the optimization procedure. In about 600 iteration steps a final design is obtained that has optimized transmission properties. Right: (482 kB) Movie of TE polarized light propagating through the topology optimized Z-bend.

Fig. 3.
Fig. 3.

The transmission for TE polarized light through the un-optimized (standard) design (black) and the optimized design (blue). The transmission spectra are based on a 2D frequency domain finite element model.

Fig. 4.
Fig. 4.

Scanning electron micrograph of the fabricated Z-bend. The number, shape and size of the holes at each bend are designed using topology optimization. The inset shows a magnified view of the optimized holes as designed (white contour) and actually fabricated.

Fig. 5.
Fig. 5.

Experimental setup used to characterize the waveguide samples.

Fig. 6.
Fig. 6.

The measured (gray) and 3D FDTD calculated (red) loss per bend for TE polarized light in the fabricated structure. Also shown is the 3D FDTD calculated bend loss for the un-optimized (black) Z-bend.

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