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Shape Optimization of microlenses

by A. Paganini and S. Sargheini and R. Hiptmair and C. Hafner

(Report number 2015-15)

Abstract
Microlenses are highly attractive for optical applications such as super resolution and photonic nanojets, but their design is more demanding than the one of larger lenses because resonance effects play an important role, which forces one to perform a full wave analysis. Although mostly spherical microlenses were studied in the past, they may have various shapes and their optimization is highly demanding, especially, when the shape is described with many parameters. We first outline a very powerful mathematical tool: shape optimization based on shape gradient computations. This procedure may be applied with much less numerical cost than traditional optimizers, especially when the number of parameters describing the shape goes to infinity. In order to demonstrate the concept, we optimize microlenses using shape optimization starting from more or less reasonable elliptical and semi-circular shapes. We show that strong increases of the performance of the lenses may be obtained for any reasonable value of the refraction index.

Copyright: the present work has been published on Optics Express and is available at the following URL .
© 2015 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

Keywords: Medical optics and biotechnology, Microscopy, Scattering, Nonspherical lens design

@Techreport{PSHH15_605,
  author = {A. Paganini and S. Sargheini and R. Hiptmair and C. Hafner},
  title = {Shape Optimization of microlenses},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-15.pdf },
  year = {2015}
}

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