Optimization and Engineering

, Volume 12, Issue 4, pp 509–534 | Cite as

Optimization of transmission spectra through periodic aperture arrays

  • David C. Dobson
  • Eddie WadbroEmail author


We investigate the problem of designing periodic aperture arrays in a thin, perfect electric conductor, such that transmission energy of time-harmonic electromagnetic plane waves through the apertures attains a specified profile with respect to frequency. We first formulate a mathematical model for the electromagnetic transmission problem, and describe a regularized numerical discretization. We then formulate the design problem as a mathematical optimization in which an objective is minimized with respect to a discrete characteristic function describing aperture shape and topology. A level-set method combined with a filtering technique and a gradient-based minimization algorithm numerically solves the problem. Several numerical examples are presented which show that although it is possible to obtain improved transmission spectra, the problem is underposed and subject to numerical instability.


Optimization Subwavelength apertures Resonantly enhanced transmission 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of Computing ScienceUmeå UniversityUmeåSweden

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