Imperial College London
Portrait Picture

DrOrySchnitzer

Faculty of Natural Sciences, Department of Mathematics

Reader in Applied Mathematics
 
 
 
//

Contact

 

+44 (0)20 7594 3833o.schnitzer Website

 
 
//

Location

 

739Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Schnitzer:2019:imamat/hxz016,
author = {Schnitzer, O},
doi = {imamat/hxz016},
journal = {IMA Journal of Applied Mathematics},
pages = {813--832},
title = {Geometric quantization of localized surface plasmons},
url = {http://dx.doi.org/10.1093/imamat/hxz016},
volume = {84},
year = {2019}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider the quasi-static problem governing the localized surface plasmon modes and permittivityeigenvaluesεof smooth, arbitrarily shaped, axisymmetric inclusions.  We develop an asymptotic theoryfor the dense part of the spectrum, i.e., close to the accumulation valueε=−1 at which a flat interfacesupports surface plasmons; in this regime, the field oscillates rapidly along the surface and decays expo-nentially away from it on a comparable scale.  Withτ=−(ε+1)as the small parameter, we developa surface-ray description of the eigenfunctions in a narrow boundary layer about the interface; the fastphase variation, as well as the slowly varying amplitude and geometric phase, along the rays are deter-mined as functions of the local geometry. We focus on modes varying at most moderately in the azimuthaldirection, in which case the surface rays are meridian arcs that focus at the two poles.  Asymptoticallymatching the diverging ray solutions with expansions valid in inner regions in the vicinities of the polesyields the quantization rule1τ∼πnΘ+12(πΘ−1)+o(1),wheren 1 is an integer andΘa geometric parameter given by the product of the inclusion length andthe reciprocal average of its cross-sectional radius along its symmetry axis. For a sphere,Θ=π, wherebythe formula returns the exact eigenvaluesε=−1−1/n. We also demonstrate good agreement with exactsolutions in the case of prolate spheroids
AU  - Schnitzer,O
DO  - imamat/hxz016
EP  - 832
PY  - 2019///
SN  - 0272-4960
SP  - 813
TI  - Geometric quantization of localized surface plasmons
T2  - IMA Journal of Applied Mathematics
UR  - http://dx.doi.org/10.1093/imamat/hxz016
UR  - http://hdl.handle.net/10044/1/71566
VL  - 84
ER  -
Download