A geometry optimization framework for photonic crystal design

E.E. Hart, A. Sóbester, K. Djidjeli, M. Molinari, K.S. Thomas, S.J. Cox

Research output: Contribution to journalArticle

Abstract

The performance of photonic crystal devices can depend strongly on their geometry. Alas, their fundamental physics offers relatively little by way of pointers in terms of optimum shapes, so numerical design search techniques must be used in an attempt to determine high performance layouts. We discuss strategies for solving this type of optimization problem, the main challenge of which is the conflict between the enormous size of the space of potentially useful designs and the relatively high computational cost of evaluating the performance of putative shapes. The optimization technique proposed here operates over increasing levels of fidelity, both in terms of the resolution of its non-parametric shape definition and in terms of the resolution of the numerical analysis of the performance of putative designs. This is a generic method, potentially applicable to any type of electromagnetic device shape design problem. We also consider a methodology for assessing the robustness of the optima generated through this process, investigating the impact of manufacturing errors on their performance. As an illustration, we apply this technology to the design of a two-dimensional photonic crystal structure; the result features a large complete band gap structure and a topology that is different from previously published designs. ?? 2011 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)25-35
Number of pages11
JournalPhotonics and Nanostructures - Fundamentals and Applications
Volume10
Issue number1
DOIs
Publication statusPublished - Jan 2012

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Photonic crystals
photonics
optimization
Geometry
geometry
crystals
dials
layouts
numerical analysis
Numerical analysis
Energy gap
topology
Physics
manufacturing
Crystal structure
Topology
methodology
electromagnetism
costs
crystal structure

Cite this

Hart, E.E. ; Sóbester, A. ; Djidjeli, K. ; Molinari, M. ; Thomas, K.S. ; Cox, S.J. / A geometry optimization framework for photonic crystal design. In: Photonics and Nanostructures - Fundamentals and Applications. 2012 ; Vol. 10, No. 1. pp. 25-35.
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A geometry optimization framework for photonic crystal design. / Hart, E.E.; Sóbester, A.; Djidjeli, K.; Molinari, M.; Thomas, K.S.; Cox, S.J.

In: Photonics and Nanostructures - Fundamentals and Applications, Vol. 10, No. 1, 01.2012, p. 25-35.

Research output: Contribution to journalArticle

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AB - The performance of photonic crystal devices can depend strongly on their geometry. Alas, their fundamental physics offers relatively little by way of pointers in terms of optimum shapes, so numerical design search techniques must be used in an attempt to determine high performance layouts. We discuss strategies for solving this type of optimization problem, the main challenge of which is the conflict between the enormous size of the space of potentially useful designs and the relatively high computational cost of evaluating the performance of putative shapes. The optimization technique proposed here operates over increasing levels of fidelity, both in terms of the resolution of its non-parametric shape definition and in terms of the resolution of the numerical analysis of the performance of putative designs. This is a generic method, potentially applicable to any type of electromagnetic device shape design problem. We also consider a methodology for assessing the robustness of the optima generated through this process, investigating the impact of manufacturing errors on their performance. As an illustration, we apply this technology to the design of a two-dimensional photonic crystal structure; the result features a large complete band gap structure and a topology that is different from previously published designs. ?? 2011 Elsevier B.V. All rights reserved.

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