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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 10 — Oct. 1, 2012
  • pp: 2935–2943

Robust topology design of periodic grating surfaces

Kasper Storgaard Friis and Ole Sigmund  »View Author Affiliations

JOSA B, Vol. 29, Issue 10, pp. 2935-2943 (2012)

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Modern nanoscale manufacturing techniques allow for a high degree of flexibility in designing surface microstructures and nanostructures. Injection molding of nanosized features allows for mass production of plastic components with a tailored nanostructure producing specific optical effects depending on the purpose. This work details the use of topology optimization for designing periodic polymer grating surfaces with complex optical properties. A method based on robust topology optimization is formulated for designing the nanostructure of plastic surfaces with extreme reflection or transmission properties. Topology optimization allows for free distribution of material but a mechanical constraint based on the fundamental free mechanical vibration frequency ensures connected structures. Several examples are given to illustrate the efficiency of the method.

© 2012 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.2770) Diffraction and gratings : Gratings
(240.6700) Optics at surfaces : Surfaces
(330.7326) Vision, color, and visual optics : Visual optics, modeling

ToC Category:
Diffraction and Gratings

Original Manuscript: June 4, 2012
Revised Manuscript: August 6, 2012
Manuscript Accepted: August 31, 2012
Published: September 28, 2012

Kasper Storgaard Friis and Ole Sigmund, "Robust topology design of periodic grating surfaces," J. Opt. Soc. Am. B 29, 2935-2943 (2012)

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  1. L. D. Chiffre, H. Kunzmann, G. N. Peggs, and D. A. Lucca, “Surfaces in precision engineering, microengineering and nanotechnology,” CIRP Ann. 52, 561–577 (2003). [CrossRef]
  2. L. Alting, F. Kimura, H. N. Hansen, and G. Bissacco, “Micro engineering,” CIRP Ann. 52, 635–657 (2003). [CrossRef]
  3. P. Utko, F. Persson, A. Kristensen, and N. B. Larsen, “Injection molded nanofluidic chips: fabrication method and functional tests using single-molecule DNA experiments,” Lab Chip 11, 303–308 (2011). [CrossRef]
  4. K. O. Andresen, M. Hansen, M. Matschuk, S. T. Jepsen, H. S. Sorensen, P. Utko, D. Selmeczi, T. S. Hansen, N. B. Larsen, N. Rozlosnik, and R. Taboryski, “Injection molded chips with integrated conducting polymer electrodes for electroporation of cells,” J. Micromech. Microeng. 20, 055010 (2010). [CrossRef]
  5. R. T. Lee and G. S. Smith, “Detailed electromagnetic simulation for the structural color of butterfly wings,” Appl. Opt. 48, 4177–4190 (2009). [CrossRef]
  6. S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97–103 (2007). [CrossRef]
  7. K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mater. 24, 2375–2379 (2012). [CrossRef]
  8. J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011). [CrossRef]
  9. D. C. Dobson, “Optimal design of periodic antireflective structures for the Helmholtz equation,” Eur. J. Appl. Math. 4, 321–339 (1993). [CrossRef]
  10. D. C. Dobson, “Optimal shape design of blazed diffraction gratings,” Appl. Math. Optim. 40, 61–78 (1999). [CrossRef]
  11. K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidisc. Optim. 42, CP11–493 (2010). [CrossRef]
  12. M. P. Bendsoe and O. Sigmund, Topology Optimisation–Theory, Methods and Applications, 2nd ed. (Springer-Verlag, 2003).
  13. 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 22, 1191–1198 (2005). [CrossRef]
  14. J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE, 2002).
  15. F. Wang, J. S. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28, 387–397 (2011). [CrossRef]
  16. J. S. Jensen, “A note on sensitivity analysis of linear dynamic systems with harmonic excitation,” Tech. rep. (Technical University of Denmark, Department of Mechanical Engineering, 2009).
  17. O. Sigmund, “Morphology-based black and white filters for topology optimization,” Struct. Multidisc. Optim. 33, 401–424 (2007). [CrossRef]
  18. J. Guest, J. Prevost, and T. Belytschko, “Achieving minimum length scale in topology optimization using nodal design variables and projection functions,” Int. J. Num. Methods Eng. 61, 238–254 (2004). [CrossRef]
  19. F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidisc. Optim. 43, 767–784 (2011). [CrossRef]
  20. O. Sigmund, “Manufacturing tolerant topology optimization,” Acta Mech. Sin. 25, 227–239 (2009). [CrossRef]
  21. K. Svanberg, “Method of moving asymptotes–a new method for structural optimization,” Int. J. Num. Methods Eng. 24, 359–373 (1987). [CrossRef]
  22. M. Schevenels, B. S. Lazarov, and O. Sigmund, “Robust topology optimization accounting for spatially varying manufacturing errors,” Comput. Methods Appl. Mech. Eng. 200, 3613–3627 (2011). [CrossRef]
  23. E. Andreassen, A. Clausen, M. Schevenels, B. S. Lazarov, and O. Sigmund, “Efficient topology optimization in MATLAB using 88 lines of code,” Struct. Multidisc. Optim. 43, 1–16 (2011). [CrossRef]
  24. J. S. Jensen, “Topology optimization of dynamics problems with Padé approximants,” Int. J. Num. Methods Eng. 72, 1605–1630 (2007). [CrossRef]

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