Open AccessHomogenization of three-dimensional metamaterial objects and validation by a fast surface-integral equation solver
Author(s) -
Xing Xiang Liu,
Jackson W. Massey,
Ming Wu,
Kristopher T. Kim,
Robert A. Shore,
Ali E. Yılmaz,
Andrea Alú
Publication year - 2013
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.21.021714
Subject(s) - homogenization (climate) , metamaterial , solver , spheres , optics , physics , integral equation , scattering , homogeneous , materials science , computational physics , mathematical analysis , statistical physics , mathematics , mathematical optimization , biodiversity , ecology , astronomy , biology
A homogenization model is applied to describe the wave interaction with finite three-dimensional metamaterial objects composed of periodic arrays of magnetodielectric spheres and is validated with full-wave numerical simulations. The homogenization is based on a dipolar model of the inclusions, which is shown to hold even in the case of densely packed arrays once weak forms of spatial dispersion and the full dynamic array coupling are taken into account. The numerical simulations are based on a fast surface-integral equation solver that enables the analysis of scattering from complex piecewise homogeneous objects. We validate the homogenization model by considering electrically large disk- and cube-shaped arrays and quantify the accuracy of the transition from an array of spheres to a homogeneous object as a function of the array size. Simulation results show that the fields scattered from large arrays with up to one thousand spheres and equivalent homogeneous objects agree well, not only far away from the arrays but also near them.