Metamaterial Design by Mesh Adaptive Direct Search
In the design of optical metamaterials, some optimization problems require launching a numerical simulation. The Mesh Adaptive Direct Search algorithm is designed for such problems. The MADS algorithm does not require any derivative information about the problem being optimized, and no continuity or differentiability assumptions are made by MADS on the functions defining the simulation. A detailed discussion of the method is provided in the second section of the chapter, followed by a discussion of the NOMAD implementation of the method and its features. The final section of the chapter lists three instances of combining NOMAD with Finite-Difference Time-Domain electromagnetic simulations to tailor the broadband spectral response and near-field interactions of Split Ring Resonator metamaterials.
KeywordsVariable Neighborhood Search Trial Point Incumbent Solution Poll Point Library Mode
Work of the first author was supported by NSERC Discovery Grant 239436-05 and AFOSR FA9550-09-1-0160.
- 17.A.J. Booker, J.E. Dennis Jr., P.D. Frank, D.B. Serafini, V. Torczon, Optimization using surrogate objectives on a helicopter test example, in Optimal Design and Control, ed. by J. Borggaard, J. Burns, E. Cliff, S. Schreck. Progress in Systems and Control Theory (Birkhäuser, Basel, 1998), pp. 49–58 Google Scholar
- 19.A. Chipouline, V. Fedotov, Coupling plasmonics with quantum systems, in SPIE Newsroom (2011) Google Scholar
- 27.R.B. Gramacy, S. Le Digabel, The mesh adaptive direct search algorithm with treed Gaussian process surrogates. Technical Report G-2011-37, Les cahiers du GERAD, 2011 Google Scholar
- 37.E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1997) Google Scholar
- 44.D. van Heesch, Doxygen manual (1997). http://www.doxygen.org/manual.html
- 45.L.N. Vicente, A.L. Custódio, Analysis of direct searches for discontinuous functions, in Mathematical Programming (2010) Google Scholar
- 46.C.J. Wang, L.Y. Lin, B.A. Parviz, 100-nm quantum dot waveguides by two-layer self-assembly, in Lasers and Electro-Optics Society, LEOS 2005. the 18th Annual Meeting of the IEEE (2005), pp. 194–195 Google Scholar