TY - GEN

T1 - Spectral problem on 3-D photonic crystals

AU - Nagatou, Kaori

AU - Brown, Malcolm

AU - Kim, Myoungnyoun

AU - Watanabe, Yoshitaka

AU - Wood, Ian

PY - 2009/11/26

Y1 - 2009/11/26

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70450179457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450179457&partnerID=8YFLogxK

U2 - 10.1063/1.3241633

DO - 10.1063/1.3241633

M3 - Conference contribution

AN - SCOPUS:70450179457

SN - 9780735407091

T3 - AIP Conference Proceedings

SP - 922

EP - 925

BT - Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009

T2 - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009

Y2 - 18 September 2009 through 22 September 2009

ER -