HOMOGENIZATION OF DIELECTRIC PHOTONIC QUASI CRYSTALS

被引：22

作者：

Bouchitte, Guy ^{[1
]}

Guenneau, Sebastien ^{[2
]}

Zolla, Frederic ^{[2
]}

机构：

[1] Univ Toulon & Var, Dept Math, Lab IMATH, F-83957 La Garde, France

[2] Univ Provence, UMR CNRS 6133, Inst Fresnel, F-13390 Marseille, France

来源：

MULTISCALE MODELING & SIMULATION | 2010年 / 8卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

two-scale convergence; cut-and-projection method; quasi crystals; scattering electromagnetism; 2-SCALE CONVERGENCE; PERIODIC-FUNCTIONS;

D O I：

10.1137/090770333

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We adapt two-scale convergence to the homogenization of photonic quasi-periodic structures such as Penrose tilings. This convergence relies upon the irrational nature of a parameter characterizing a quasi-crystalline phase through its associated cut-and-projection matrix of permittivity: We generate quasi crystals by considering a periodic structure in an upper-dimensional space. We apply this tool to the homogenization of the vector Maxwell system.

引用

页码：1862 / 1881

页数：20

共 36 条

[1] HOMOGENIZATION AND 2-SCALE CONVERGENCE
ALLAIRE, G
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (06) : 1482 - 1518
[2] [Anonymous], 1988, Functional and variational methods
[3] [Anonymous], 1978, ASYMPTOTIC ANAL PERI
[4] BAKHALOV N, 1989, HOMOGENIZATION AVERA
[5] Besicovitch AS, 1926, P LOND MATH SOC, V25, P495
[6] Bohr H, 1924, ACTA MATH-DJURSHOLM, V45, P29
[7] On the theory of fast periodic functions. II. Connection of fast periodic functions with functions that have many infinite variables; equal approximations using trigonometric sums.
Bohr, H
[J]. ACTA MATHEMATICA, 1925, 46 (1-2) : 101 - 214
[8] Bondarenko A, 2005, DISCRETE CONT DYN-A, V13, P503
[9] Homogenization of a wire photonic crystal:: The case of small volume fraction
Bouchitte, Guy
Felbacq, Didier
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (06) : 2061 - 2084
[10] Bourgeat A, 1999, ASYMPTOTIC ANAL, V21, P303

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