Optimal localization of eigenfunctions in an inhomogeneous medium

David C. Dobson, Fadil Santosa

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The problem of creating eigenfunctions which are localized arises in the study of photonic bandgap structures. A model problem, that of finding material inhomogeneity in a domain so that one of its Dirichlet eigenfunctions is localized, is considered in this work. The most difficult aspect, that of formulating the problem, is described, and well-posed variational problems are given. A computational approach, based on gradient descent with projection and trajectory continuation, is devised to solve the optimization problem. Numerical examples are provided which demonstrate the capability of the computational method.

Original languageEnglish (US)
Pages (from-to)762-774
Number of pages13
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - 2004


  • Defect modes
  • Mode localization
  • Optimal design


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