TY - JOUR
T1 - Fundamental correction of Mie's scattering theory for the analysis of the plasmonic resonance of a metal nanosphere
AU - Fujii, Masafumi
PY - 2014/3/6
Y1 - 2014/3/6
N2 - It is shown that Mie's solution to Maxwell's equations no longer holds for the analysis of resonance of a plasmonic metal nanosphere. The conventional Mie's solution is based on the spherical Bessel and the spherical Hankel functions of an outgoing wave, whereas the permittivity of metals of a negative real part leads to a phase velocity that directs inward to the sphere, which is opposite from the direction of the energy flow as often discussed for negative-index metamaterials. This is a fundamental problem overlooked for a long time; a correction can be found from the viewpoint of a time-reversal problem involving negative permittivity media. The continuity of the field solution at the sphere surface is shown to be corrected by replacing the spherical Hankel function of an outgoing wave with that of an incoming wave, i.e., by adopting the complex conjugate of the conventional solutions. The corrected theory has been verified by the analyses of various metal nanospheres. In addition, the derivation of the scattering cross sections based on the corrected theory has elucidated that the conservation law of energy holds and that, more importantly, the conventional Mie's solution gives the same amplitude of the cross sections when they are obtained for real, not complex, frequency.
AB - It is shown that Mie's solution to Maxwell's equations no longer holds for the analysis of resonance of a plasmonic metal nanosphere. The conventional Mie's solution is based on the spherical Bessel and the spherical Hankel functions of an outgoing wave, whereas the permittivity of metals of a negative real part leads to a phase velocity that directs inward to the sphere, which is opposite from the direction of the energy flow as often discussed for negative-index metamaterials. This is a fundamental problem overlooked for a long time; a correction can be found from the viewpoint of a time-reversal problem involving negative permittivity media. The continuity of the field solution at the sphere surface is shown to be corrected by replacing the spherical Hankel function of an outgoing wave with that of an incoming wave, i.e., by adopting the complex conjugate of the conventional solutions. The corrected theory has been verified by the analyses of various metal nanospheres. In addition, the derivation of the scattering cross sections based on the corrected theory has elucidated that the conservation law of energy holds and that, more importantly, the conventional Mie's solution gives the same amplitude of the cross sections when they are obtained for real, not complex, frequency.
UR - http://www.scopus.com/inward/record.url?scp=84897862352&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.89.033805
DO - 10.1103/PhysRevA.89.033805
M3 - 学術論文
AN - SCOPUS:84897862352
SN - 1050-2947
VL - 89
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 3
M1 - 033805
ER -