### 抜粋

In this research we will study some fundamental mathematical properties of photonic crystals which have many applications in optics and nanotechnology. A good model for these crystals is described by the Maxwell's equations with periodic electric permittivity. The spectral problem for Maxwell's equations possesses bands of essential spectrum which may be separated by gaps. Waves of a frequency in such a gap cannot propagate in the crystal, while other frequencies can. This makes photonic crystals very interesting for applications in nanotechnology and other areas. It is important not just to have quantitative numerical evidence for the location of these gaps, but to be able to prove the existence of spectral gaps with mathematical certainty. We propose to use computer assisted methods to achieve this.

元の言語 | 英語 |
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ホスト出版物のタイトル | Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 |

ページ | 922-925 |

ページ数 | 4 |

DOI | |

出版物ステータス | 出版済み - 11 26 2009 |

イベント | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, ギリシャ 継続期間: 9 18 2009 → 9 22 2009 |

### 出版物シリーズ

名前 | AIP Conference Proceedings |
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巻 | 1168 |

ISSN（印刷物） | 0094-243X |

ISSN（電子版） | 1551-7616 |

### その他

その他 | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 |
---|---|

国 | ギリシャ |

市 | Rethymno, Crete |

期間 | 9/18/09 → 9/22/09 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### これを引用

*Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009*(pp. 922-925). (AIP Conference Proceedings; 巻数 1168). https://doi.org/10.1063/1.3241633