A non-asymptotic homogenization theory for periodic electromagnetic structures

Homogenization of electromagnetic periodic composites is treated as a two-scale problem and solved by approximating the fields on both scales with eigenmodes that satisfy Maxwell's equations and boundary conditions as accurately as possible. Built into this homogenization methodology is an error indicator whose value characterizes the accuracy of homogenization. The proposed theory allows one to define not only bulk, but also position-dependent material parameters (e.g. in proximity to a physical boundary) and to quantify the trade-off between the accuracy of homogenization and its range of applicability to various illumination conditions.

[1]  S. Arridge,et al.  Optical tomography: forward and inverse problems , 2009, 0907.2586.

[2]  I. Tsukerman.  Nonlocal homogenization of metamaterials by dual interpolation of fields , 2011 .

[3]  R. V. Craster,et al.  High-frequency homogenization for periodic media , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[4]  I. Tsukerman,et al.  Electromagnetic applications of a new finite-difference calculus , 2005, IEEE Transactions on Magnetics.

[5]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.

[6]  S. Feng.  Graphical retrieval method for orthorhombic anisotropic materials. , 2010, Optics express.

[7]  C. Simovski,et al.  Material parameters of metamaterials (a Review) , 2009 .

[8]  Ralf Hiptmair,et al.  Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations , 2011, Math. Comput..

[9]  F. Cajko,et al.  Photonic Band Structure Computation Using FLAME , 2008, IEEE Transactions on Magnetics.

[10]  Igor Tsukerman,et al.  Computational Methods for Nanoscale Applications: Particles, Plasmons and Waves , 2007 .

[11]  Igor Tsukerman,et al.  Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation , 2011 .

[12]  Igor Tsukerman,et al.  A class of difference schemes with flexible local approximation , 2006 .

[13]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[14]  Jin Au Kong,et al.  Robust method to retrieve the constitutive effective parameters of metamaterials. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Sylvain Baillet,et al.  Forward and Inverse Problems of MEG/EEG , 2014, Encyclopedia of Computational Neuroscience.

[16]  Sébastien Guenneau,et al.  Bloch dispersion and high frequency homogenization for separable doubly-periodic structures , 2012 .

[17]  Effective constitutive parameters of plasmonic metamaterials: homogenization by dual field interpolation. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Milton.  The Theory of Composites , 2002 .

[19]  C. Scheiber,et al.  A Model Order Reduction Method for Efficient Band Structure Calculations of Photonic Crystals , 2010, IEEE Transactions on Magnetics.

[20]  D. Smith,et al.  Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Igor Tsukerman,et al.  Current-driven homogenization and effective medium parameters for finite samples , 2013 .

[22]  Refraction and rightness in photonic crystals. , 2005, Optics express.

[23]  Constantin R. Simovski,et al.  On electromagnetic characterization and homogenization of nanostructured metamaterials , 2010 .

[24]  Vadim A. Markel,et al.  Homogenization of Maxwell's equations in periodic composites: boundary effects and dispersion relations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Carsten Rockstuhl,et al.  Retrieving effective parameters for metamaterials at oblique incidence , 2008 .

[26]  D. Felbacq,et al.  Anomalous homogeneous behaviour of metallic photonic crystals , 2000 .

[27]  R. McPhedran,et al.  Modeling photonic crystal interfaces and stacks: impedance-based approaches , 2013 .

[28]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[29]  Ismael Herrera,et al.  Trefftz Method: A General Theory , 2000 .

[30]  A. Moiola.  Trefftz-discontinuous Galerkin methods for time-harmonic wave problems , 2011 .

[31]  Vadim A. Markel,et al.  Surface waves in three-dimensional electromagnetic composites and their effect on homogenization. , 2013, Optics express.