Topology optimization and fabrication of photonic crystal structures

doi:10.1364/OPEX.12.001996

Optics Express

Editor: Michael Duncan
Vol. 12, Iss. 9 — May. 3, 2004
pp: 1996–2001

Topology optimization and fabrication of photonic crystal structures

P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund »View Author Affiliations

Optics Express, Vol. 12, Issue 9, pp. 1996-2001 (2004)
http://dx.doi.org/10.1364/OPEX.12.001996

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References (19)
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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.

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves
(130.3130) Integrated optics : Integrated optics materials
(220.4830) Optical design and fabrication : Systems design
(230.5440) Optical devices : Polarization-selective devices
(230.7390) Optical devices : Waveguides, planar

ToC Category:
Research Papers

History
Original Manuscript: March 30, 2004
Revised Manuscript: April 23, 2004
Published: May 3, 2004

Citation
P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, "Topology optimization and fabrication of photonic crystal structures," Opt. Express 12, 1996-2001 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-9-1996

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References

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]
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]
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).
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]
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]
M. P. Bendsøe and O. Sigmund, Topology optimization �?? Theory, Methods and Applications (Springer-Verlag, 2003).
T. P. Felici and D. F. G. Gallagher, �??Improved waveguide structures derived from new rapid optimization techniques,�?? Proc. SPIE 4986, 375-385 (2003). [CrossRef]
J. Smajic, C. Hafner and 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]
W. J. Kim and J. D. O�??Brien, �??Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite element method,�?? J. Opt. Soc. Am. B 21, 289-295 (2004). [CrossRef]
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]
T. Uusitupa, K. Kärkkäinen and K. Nikoskinen, �??Studying 120° PBG waveguide bend using FDTD,�?? Microwave Opt. Technol. Lett. 39, 326-333 (2003). [CrossRef]
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.
K. Svanberg, �??The method of moving asymptotes: a new method for structural optimization,�?? Int. J. Numer. Meth. Engng. 24, 359-373 (1987). [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]
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]
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, T. Niemi, and H. M. H. Chong, �??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]

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

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

[3] 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]

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

[5] 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).

[6] 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]

[7] 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]

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

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

[10] J. Smajic, C. Hafner and 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]

[11] W. J. Kim and J. D. O�??Brien, �??Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite element method,�?? J. Opt. Soc. Am. B 21, 289-295 (2004). [CrossRef]

[12] 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]

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

[14] 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.

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

[16] 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]

[17] 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]

[18] 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]

[19] A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, T. Niemi, and H. M. H. Chong, �??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]

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Topology optimization and fabrication of photonic crystal structures