Tailoring dispersion properties of photonic crystal waveguides by topology optimization

Waves in Random and Complex Media

Volumn 17, Issue 4, 2007, Pages 477-489

  Stainko, R ^a   Sigmund, O ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSION COMPENSATION; FREQUENCY DOMAIN ANALYSIS; GRADIENT METHODS; GROUP VELOCITY DISPERSION; SENSITIVITY ANALYSIS; SHAPE OPTIMIZATION; WAVEGUIDES;

DISPERSION PROPERTIES;

PHOTONIC CRYSTALS;

EID: 35548930696     PISSN: 17455030     EISSN: 17455049     Source Type: Journal    
DOI: 10.1080/17455030701501851     Document Type: Article

References (24)

1. Russell, P. St. J., Marin, E., Diez, A., Guenneau, S. and Movchan, A. B. (2003) Sonic band gaps in pcf preforms: Enhancing the interaction of sound and light. Optics Express, 11, pp. 2550-2560.
2. Povinelli, M. L. (2006) Slow light: Variable speed limit. Nature Physics, 2, pp. 735-736.
3. Mok, J. T., de Sterke, C. M., Littler, I. C. M. and Eggleton, B. J. (2006) Dispersionless slow light using gap solitons. Nature Physics, 2, pp. 775-780.
4. Settle, M. D., Engelen, R. J. P., Salib, M., Michaeli, A., Kuipers, L. and Krauss, T. F. (2007) Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth. Optics Express, 15, pp. 219-226.
5. Notomi, M., Yamada, K., Shinya, A., Takahashi, J., Takahashi, C. and Yokohama, I. (2001) Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs. Physical Review Letters, 87, pp. 253902/1-253902/4.
6. Johnson, S. G., Villeneuve, P. R., Fan, S. and Joannopoulos, J. D. (2000) Linear waveguides in photonic-crystal slabs. Physical Review B (Condensed Matter), 62, pp. 8212-8222.
7. Soljacic, M., Johnson, S. G., Fan, Sh., Ibanescu, M., Ippen, E. and Joannopoulos, J. D. (2002) Photonic-crystal slow-light enhancement of nonlinear phase sensitivity. Journal of the Optical Society of America B: Optical Physics, 19, pp. 2052-2059.
8. Petrov, A. Y. and Eich, M. (2004) Zero dispersion at small group velocities in photonic crystal waveguides. Applied Physics Letters, 85, pp. 4866-4868.
9. Mori, D. and Baba, T. (2004) Dispersion-controlled optical group delay device by chirped photonic crystal waveguides. Applied Physics Letters, 85, pp. 1101-1103.
10. Frandsen, L. H., Lavrinenko, A. V., Fage-Pedersen, J. and Borel, P. I. (2006) Photonic crystal waveguides with semi-slow light and tailored dispersion properties. Optics Express, 14, pp. 9444-9450.
11. Xia, F., Sekaric, L. and Vlasov, Y. (2007) Ultracompact optical buffers on a silicon chip. Nature Photonics, 1, pp. 65-71.
12. Tanabe, T., Notomi, M., Kuramochi, E., Shinya, A. and Taniyama, H. (2007) Trapping and delaying photons for one nanosecond in an ultrasmall high-q photonic-crystal nanocavity. Nature Photonics, 1, pp. 49-52.
13. Bendsøe, M. P. and Kikuchi, N. (1988) Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71, pp. 197-224.
14. Bendsøe, M. P. and Sigmund, O. (2004) Topology Optimization - Theory, Methods, and Applications, Springer Verlag, Berlin
15. Cox, S. J. and Dobson, D. C. (1999) Maximizing band gaps in two-dimensional photonic crystals. SIAM Journal for Applied Mathematics, 59, pp. 2108-2120.
16. Sigmund, O. and Jensen, J. S. (2003) Systematic design of phononic band gap materials and structures by topology optimization. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 361, pp. 1001-1019.
17. Jensen, J. S. and Sigmund, O. (2004) Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends. Applied Physics Letters, 84, pp. 2022-2024.
18. Borel, P. I., Harpøth, A., Frandsen, L. H., Kristensen, M., Jensen, J. S., Shi, P. and Sigmund, O. (2004) Topology optimization and fabrication of photonic crystal structures. Optics Express, 12, pp. 1996-2001.
19. Jensen, J. S. and Sigmund, O. (2005) Topology optimization of photonic crystal structures: A high-bandwidth low-loss T-junction waveguide. Journal of the Optical Society of America B: Optical Physics, 22, pp. 1191-1198.
20. Borel, P. I., Frandsen, L. H., Harpøth, A., Kristensen, M., Jensen, J. S. and Sigmund, O. (2005) Topology optimised broadband photonic crystal Y-splitter. Electronics Letters, 41, pp. 69-71.
21. Cook, R. D., Malkus, D. S., Plesha, M. E. and Witt, R. J. (2002) Concepts and Applications of Finite Element Analysis, John Wiley, New York
22. Svanberg, K. (1987) The Method of Moving Asymptotes - A new method for structural optimization. International Journal for Numerical Methods in Engineering, 24, pp. 359-373.
23. Sigmund, O. and Petersson, J. (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization, 16, pp. 68-75.
24. Sigmund, O. (2007) Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization, 33, pp. 401-424.