CREATING BAND GAPS IN PERIODIC MEDIA

被引：8

作者：

Lipton, Robert ^{[1
]}

Viator, Robert, Jr. ^{[2
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Univ Minnesota, Inst Math & Its Applicat, Minneapolis, MN 55455 USA

来源：

MULTISCALE MODELING & SIMULATION | 2017年 / 15卷 / 04期

关键词：

spectral theory; band gaps; photonics; periodic media; DENSITY-OF-STATES; DIELECTRIC-CONSTANT; SPECTRAL PROPERTIES; BLOCH WAVES; OPERATORS; CRYSTALS; BOUNDS;

D O I：

10.1137/16M1083396

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We identify explicit conditions on geometry and material contrast for creating band gaps in 2-d photonic and 3-d acoustic crystals. This approach is novel and makes use of the electro-static and quasi-periodic source free resonances of the crystal. The source free modes deliver a spectral representation for solution operators associated with propagation of electromagnetic and acoustic waves inside periodic high contrast media. An accurate characterization of the quasi-periodic and electrostatic resonance spectrum in terms of the shape and geometry of the scatters is possible. This information together with the Dirichlet and a Neumann like spectra associated with the inclusions deliver conditions sufficient for opening band gaps at finite contrast. The theory provides a systematic means for the identification of photonic and phononic band gaps within a specified frequency range.

引用

页码：1612 / 1650

页数：39

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