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Topology optimization of periodic layouts of dielectric materials

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Abstract

A topology optimization method is used to design two dimensional periodic structures with desirable transmission properties by distributing two materials of different permittivity over a rectangular representative cell. A plane wave expansion of the electric field at the input and output boundaries is used in the analysis. This allows non-homogeneous material distributions near the boundaries. Numerical examples are used to verify the robustness of the method and to investigate the importance of retaining higher modes in the expansions. It is found that the optimization problem typically admits possibly many local optima and the relevance of higher modes depends on the nature of the solution found. In some instances, higher modes play an important role and using only the dominant mode in the analysis is shown to result in errors in the evaluation of the performance of the design.

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Acknowledgement

This material is based upon work supported, in part, by the US National Science Foundation under Grant No. 0800388. This support is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Michigan State University, East Lansing, MI, 48824-1226, USA

    Kazuko Fuchi & Alejandro R. Diaz

  2. Department of Electrical and Computer Engineering, College of Engineering, Michigan State University, East Lansing, MI, 48824-1226, USA

    Edward Rothwell, Raoul Ouedraogo & Andrew Temme

Authors
  1. Kazuko Fuchi
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  2. Alejandro R. Diaz
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  3. Edward Rothwell
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  4. Raoul Ouedraogo
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  5. Andrew Temme
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Corresponding author

Correspondence to Alejandro R. Diaz.

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Fuchi, K., Diaz, A.R., Rothwell, E. et al. Topology optimization of periodic layouts of dielectric materials. Struct Multidisc Optim 42, 483–493 (2010). https://doi.org/10.1007/s00158-010-0522-x

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  • DOI: https://doi.org/10.1007/s00158-010-0522-x

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