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Mathematical and Computational Methods in Photonics and Phononics

by H. Ammari and B. Fitzpatrick and H. Kang and M. Ruiz and S. Yu and H. Zhang

(Report number 2017-05)

Abstract
The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, and its technological applications. The aim of this book is to review new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing subwavelength resonators; super-focusing and super-resolution of electromagnetic and acoustic waves; photonic and phononic crystals; electromagnetic cloaking; and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, we demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. The book could be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems. Researchers in photonics, phononics, and nanotechnologies might also find this book helpful.

Keywords: nanophotonics, diffractive optics, photonic crystals, plasmonic resonance, Minnaert bubble, Helmholtz resonator, metamaterials, superresolution, subwavelength resonator, electromagnetic invisibility, cloaking, layer potentials, asymptotic analysis, Gohberg-Sigal's theory.

@Techreport{AFKRYZ17_701,
  author = {H. Ammari and B. Fitzpatrick and H. Kang and M. Ruiz and S. Yu and H. Zhang},
  title = {Mathematical and Computational Methods in Photonics and Phononics},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-05.pdf },
  year = {2017}
}

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