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 -